Vinod K. Wadhawan
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199229178
- eISBN:
- 9780191711282
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199229178.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter discusses ferroic materials, which are the first of the three types of nonlinear-response materials discussed in this book, the other two being soft materials and nanostructured ...
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This chapter discusses ferroic materials, which are the first of the three types of nonlinear-response materials discussed in this book, the other two being soft materials and nanostructured materials. Their nonlinear properties are a consequence of one or more ferroic phase transitions that can occur in them. The chapter begins with an introduction to phase transitions and critical phenomena in crystals. Ferroic phase transitions are those that involve a change of point-group symmetry in a nondisruptive manner. Their thermodynamic classification is described, which helps divide ferroic materials into ferroelectrics, ferromagnetics, ferroelastics, ferrobielastics, ferroelastoelectrics, etc. The poling process for ferroic ceramics is explained. The domain structure of ferroics, and the possibilities of tailoring this structure to advantage are discussed. The importance of multiferroics in smart-structures research is emphasized. There are also sections on spin-glasses, shape-memory alloys and ceramics, and relaxor ferroelectrics. The book has helpful appendices on crystallographic symmetry and on tensor properties.Less
This chapter discusses ferroic materials, which are the first of the three types of nonlinear-response materials discussed in this book, the other two being soft materials and nanostructured materials. Their nonlinear properties are a consequence of one or more ferroic phase transitions that can occur in them. The chapter begins with an introduction to phase transitions and critical phenomena in crystals. Ferroic phase transitions are those that involve a change of point-group symmetry in a nondisruptive manner. Their thermodynamic classification is described, which helps divide ferroic materials into ferroelectrics, ferromagnetics, ferroelastics, ferrobielastics, ferroelastoelectrics, etc. The poling process for ferroic ceramics is explained. The domain structure of ferroics, and the possibilities of tailoring this structure to advantage are discussed. The importance of multiferroics in smart-structures research is emphasized. There are also sections on spin-glasses, shape-memory alloys and ceramics, and relaxor ferroelectrics. The book has helpful appendices on crystallographic symmetry and on tensor properties.
Nasr Ghoniem and Daniel Walgraef
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199298686
- eISBN:
- 9780191720222
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199298686.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
In materials, critical phenomena such as phase transitions, plastic deformation and fracture are intimately related to self-organization. Understanding the origin of spatio-temporal order in systems ...
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In materials, critical phenomena such as phase transitions, plastic deformation and fracture are intimately related to self-organization. Understanding the origin of spatio-temporal order in systems far from thermal equilibrium and the selection mechanisms of spatial structures and their symmetries is a major theme of present day research on the structure of continuous matter. Furthermore, the development of methods for producing spatially-ordered and self-assembled microstructure in solids by non-equilibrium methods opens the door to many technological applications. In order to describe and understand the behaviour of such materials, dynamical concepts related to non-equilibrium phenomena, irreversible thermodynamics, nonlinear dynamics, and bifurcation theory, are required. The generic presence of defects and their crucial influence on pattern formation and critical phenomena in extended systems is now well-established. Similar to observations in hydrodynamical, liquid crystal, and laser systems, defects in materials have a profound effect. This book is divided into two volumes. The first volume is devoted to the most basic concepts of the physics, mechanics, and mathematical theory utilized in the analysis of non-equilibrium materials. The book presents a background on material deformation, defect theory, transport processes, and the statistical mechanics and thermodynamics of phase transitions. Mathematical concepts of non-linear dynamics, such as bifurcation and instability theory, the dynamics of complex systems near pattern forming instabilities, the generic aspects of pattern formation, selection and stability are presented. Stochastic and numerical methods used in this field are also introduced. The methods and techniques developed in the first volume are applied in the second volume to specific problems in various advanced technologies.Less
In materials, critical phenomena such as phase transitions, plastic deformation and fracture are intimately related to self-organization. Understanding the origin of spatio-temporal order in systems far from thermal equilibrium and the selection mechanisms of spatial structures and their symmetries is a major theme of present day research on the structure of continuous matter. Furthermore, the development of methods for producing spatially-ordered and self-assembled microstructure in solids by non-equilibrium methods opens the door to many technological applications. In order to describe and understand the behaviour of such materials, dynamical concepts related to non-equilibrium phenomena, irreversible thermodynamics, nonlinear dynamics, and bifurcation theory, are required. The generic presence of defects and their crucial influence on pattern formation and critical phenomena in extended systems is now well-established. Similar to observations in hydrodynamical, liquid crystal, and laser systems, defects in materials have a profound effect. This book is divided into two volumes. The first volume is devoted to the most basic concepts of the physics, mechanics, and mathematical theory utilized in the analysis of non-equilibrium materials. The book presents a background on material deformation, defect theory, transport processes, and the statistical mechanics and thermodynamics of phase transitions. Mathematical concepts of non-linear dynamics, such as bifurcation and instability theory, the dynamics of complex systems near pattern forming instabilities, the generic aspects of pattern formation, selection and stability are presented. Stochastic and numerical methods used in this field are also introduced. The methods and techniques developed in the first volume are applied in the second volume to specific problems in various advanced technologies.
Frank H. Herbstein
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198526605
- eISBN:
- 9780191712142
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526605.003.0016
- Subject:
- Physics, Crystallography
Thermodynamic measurements for a limited sample of crystalline mixed-stack 1:1 π-molecular compounds show that most are enthalpy-stabilized, some entropy-stabilized, and a few both enthalpy and ...
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Thermodynamic measurements for a limited sample of crystalline mixed-stack 1:1 π-molecular compounds show that most are enthalpy-stabilized, some entropy-stabilized, and a few both enthalpy and entropy-stabilized. Correlation of these thermodynamic results with crystal structures remains a task for the future. Combination of optical spectroscopic methods at very low temperatures and electron spin resonance measurements have provided proof of Mulliken’s theory also for the solid state. The room temperature crystal structures of 1:1 π-molecular compounds are not necessarily representative of the entire range of pressure-temperature behaviour of these materials. There are often hints of disorder (usually of the donor) in the room temperature structures, and these have been correlated for a few systems with disorder-to-order transitions (thermodynamically second-order, following Ehrenfest) that occur on cooling. These have been studied by a combination of calorimetric, diffraction, and resonance techniques. Despite overall similarities, each system surveyed has its own individual characteristics. A number of 1:1 π-molecular compounds have been shown to transform to quasi-plastic phases on heating. A small number of mixed stack 1:1 π-molecular compounds with neutral ground states have been shown to transform to ionic structures on cooling or application of pressure.Less
Thermodynamic measurements for a limited sample of crystalline mixed-stack 1:1 π-molecular compounds show that most are enthalpy-stabilized, some entropy-stabilized, and a few both enthalpy and entropy-stabilized. Correlation of these thermodynamic results with crystal structures remains a task for the future. Combination of optical spectroscopic methods at very low temperatures and electron spin resonance measurements have provided proof of Mulliken’s theory also for the solid state. The room temperature crystal structures of 1:1 π-molecular compounds are not necessarily representative of the entire range of pressure-temperature behaviour of these materials. There are often hints of disorder (usually of the donor) in the room temperature structures, and these have been correlated for a few systems with disorder-to-order transitions (thermodynamically second-order, following Ehrenfest) that occur on cooling. These have been studied by a combination of calorimetric, diffraction, and resonance techniques. Despite overall similarities, each system surveyed has its own individual characteristics. A number of 1:1 π-molecular compounds have been shown to transform to quasi-plastic phases on heating. A small number of mixed stack 1:1 π-molecular compounds with neutral ground states have been shown to transform to ionic structures on cooling or application of pressure.
Hidetoshi Nishimori and Gerardo Ortiz
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577224
- eISBN:
- 9780191722943
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577224.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into ...
More
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.Less
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.
Antônio M. Figueiredo Neto and Silvio R. A. Salinas
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198525509
- eISBN:
- 9780191711756
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525509.001.0001
- Subject:
- Physics, Crystallography
Mixtures of surfactant or amphiphilic molecules and solvents are known to display a large number of lyotropic mesophases. Although the physics of thermotropic liquid crystals has been vastly ...
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Mixtures of surfactant or amphiphilic molecules and solvents are known to display a large number of lyotropic mesophases. Although the physics of thermotropic liquid crystals has been vastly discussed in the literature, lyotropic mesophases have been much less explored. This book gives a unifying presentation of the structural and physical properties of lyotropic liquid crystalline systems, including a set of experimental results and a discussion of the characterization of different structures and the corresponding phase transitions. The initial chapters contain a description of the main experimental results and techniques associated with the characterization of lyotropic mixtures, and an overview of some theoretical approaches to account for the phase transitions and phase diagrams of these mesophases. This book includes discussions on periodically organized lyotropic systems, micellar and bicontinuous structures, modulated and cholesteric structures, and a number of related developments (magnetic colloids, microemulsions, films, and lyo-banana mesophases).Less
Mixtures of surfactant or amphiphilic molecules and solvents are known to display a large number of lyotropic mesophases. Although the physics of thermotropic liquid crystals has been vastly discussed in the literature, lyotropic mesophases have been much less explored. This book gives a unifying presentation of the structural and physical properties of lyotropic liquid crystalline systems, including a set of experimental results and a discussion of the characterization of different structures and the corresponding phase transitions. The initial chapters contain a description of the main experimental results and techniques associated with the characterization of lyotropic mixtures, and an overview of some theoretical approaches to account for the phase transitions and phase diagrams of these mesophases. This book includes discussions on periodically organized lyotropic systems, micellar and bicontinuous structures, modulated and cholesteric structures, and a number of related developments (magnetic colloids, microemulsions, films, and lyo-banana mesophases).
Andrea Braides
- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198507840
- eISBN:
- 9780191709890
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507840.003.0016
- Subject:
- Mathematics, Applied Mathematics
This chapter presents a self-contained account of the slicing method that allows the exhibition of a lower bound for high-dimensional problems through their one-dimensional sections. After computing ...
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This chapter presents a self-contained account of the slicing method that allows the exhibition of a lower bound for high-dimensional problems through their one-dimensional sections. After computing a family of one-dimensional limit problems, an optimization is performed through an argument characterizing the supremum of a family of measures. The upper inequality is obtained by a density argument whenever recovery sequences have a one-dimensional form. This method can be applied to the high-dimensional gradient theory of phase transitions.Less
This chapter presents a self-contained account of the slicing method that allows the exhibition of a lower bound for high-dimensional problems through their one-dimensional sections. After computing a family of one-dimensional limit problems, an optimization is performed through an argument characterizing the supremum of a family of measures. The upper inequality is obtained by a density argument whenever recovery sequences have a one-dimensional form. This method can be applied to the high-dimensional gradient theory of phase transitions.
M. E. LINES and A. M. GLASS
- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198507789
- eISBN:
- 9780191709944
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507789.003.0008
- Subject:
- Physics, Condensed Matter Physics / Materials
A very important group of ferroelectrics is that known as the perovskites from the mineral perovskite CaTiO3 (which itself is actually a distorted perovskite structure). The perfect perovskite ...
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A very important group of ferroelectrics is that known as the perovskites from the mineral perovskite CaTiO3 (which itself is actually a distorted perovskite structure). The perfect perovskite structure is an extremely simple one with general formula ABO3, where A is a monovalent or divalent metal and B is a tetra- or pentavalent one. The off-centring of the B-cation is a relatively independent process that can occur in any structure built from the hard octahedra. It is this off-centering which leads to the presence of dipoles and to both ferroelectricity and antiferroelectricity. This chapter looks at the oxygen octahedron and the ferroelectric perovskites, including barium titanate, potassium niobate, potassium tantalate niobate, lead titanate, sodium niobate, potassium tantalate, and strontium titanate. Antiferroelectric and cell-doubling perovskites such as lead zirconate and lithium tantalate are also discussed, along with zone-boundary lattice-mode condensation, local-mode analysis, low-temperature polarization, stoichiometry, tungsten-bronze-type structures, and diffuse phase transitions.Less
A very important group of ferroelectrics is that known as the perovskites from the mineral perovskite CaTiO3 (which itself is actually a distorted perovskite structure). The perfect perovskite structure is an extremely simple one with general formula ABO3, where A is a monovalent or divalent metal and B is a tetra- or pentavalent one. The off-centring of the B-cation is a relatively independent process that can occur in any structure built from the hard octahedra. It is this off-centering which leads to the presence of dipoles and to both ferroelectricity and antiferroelectricity. This chapter looks at the oxygen octahedron and the ferroelectric perovskites, including barium titanate, potassium niobate, potassium tantalate niobate, lead titanate, sodium niobate, potassium tantalate, and strontium titanate. Antiferroelectric and cell-doubling perovskites such as lead zirconate and lithium tantalate are also discussed, along with zone-boundary lattice-mode condensation, local-mode analysis, low-temperature polarization, stoichiometry, tungsten-bronze-type structures, and diffuse phase transitions.
Xiao-Gang Wen
- Published in print:
- 2007
- Published Online:
- February 2010
- ISBN:
- 9780199227259
- eISBN:
- 9780191713019
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227259.003.03
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter introduces a quantum field theory for interacting boson systems. It develops a mean-field theory to study the superfluid phase. A path integral formulation is then developed to re-derive ...
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This chapter introduces a quantum field theory for interacting boson systems. It develops a mean-field theory to study the superfluid phase. A path integral formulation is then developed to re-derive the superfuid phase, which results in a low energy effective non-linear sigma model. A renormalization group approach is introduced to study the zero temperature quantum phase transition between superfluid and Mott insulator phase, and finite temperature phase transition between superfluid and normal phase. The physics and the importance of symmetry breaking in phase transitions and in protecting gapless excitations are discussed. The phenomenon of superfluidity and superconductivity is also discussed, where the coupling to U(1) gauge field is introduced.Less
This chapter introduces a quantum field theory for interacting boson systems. It develops a mean-field theory to study the superfluid phase. A path integral formulation is then developed to re-derive the superfuid phase, which results in a low energy effective non-linear sigma model. A renormalization group approach is introduced to study the zero temperature quantum phase transition between superfluid and Mott insulator phase, and finite temperature phase transition between superfluid and normal phase. The physics and the importance of symmetry breaking in phase transitions and in protecting gapless excitations are discussed. The phenomenon of superfluidity and superconductivity is also discussed, where the coupling to U(1) gauge field is introduced.
Antônio M. Figueiredo Neto and Silvio R. A. Salinas
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198525509
- eISBN:
- 9780191711756
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525509.003.0004
- Subject:
- Physics, Crystallography
This chapter discusses phase diagrams and phase transitions in lyotropic liquid crystals from the point of view of symmetry transformations between periodically ordered structures. In some systems, ...
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This chapter discusses phase diagrams and phase transitions in lyotropic liquid crystals from the point of view of symmetry transformations between periodically ordered structures. In some systems, amphiphilic aggregates may suffer a drastic reorganization, with modifications of geometry, and without a group-subgroup relation between the newly formed and the initial structures. There are some examples of these reconstructive phase transitions involving lamellar, hexagonal, cubic, and sponge phases. In other cases, there are equilibrium group-subgroup relations between different structures, as in the weak first-order nematic-isotropic transitions, which are quite well described by the Landau expansion. On the basis of proposals by Mettout, Toledano, and co-workers, the chapter presents a discussion of an extension of the standard Landau approach, which is adequate to account for the reconstructive phase transitions. In particular, there are examples of lamellar-tetragonal, lamellar-cubic, and lamellar-hexagonal transitions, and discussions of direct and reversed mesophases.Less
This chapter discusses phase diagrams and phase transitions in lyotropic liquid crystals from the point of view of symmetry transformations between periodically ordered structures. In some systems, amphiphilic aggregates may suffer a drastic reorganization, with modifications of geometry, and without a group-subgroup relation between the newly formed and the initial structures. There are some examples of these reconstructive phase transitions involving lamellar, hexagonal, cubic, and sponge phases. In other cases, there are equilibrium group-subgroup relations between different structures, as in the weak first-order nematic-isotropic transitions, which are quite well described by the Landau expansion. On the basis of proposals by Mettout, Toledano, and co-workers, the chapter presents a discussion of an extension of the standard Landau approach, which is adequate to account for the reconstructive phase transitions. In particular, there are examples of lamellar-tetragonal, lamellar-cubic, and lamellar-hexagonal transitions, and discussions of direct and reversed mesophases.
Stephen J. Blundell and Katherine M. Blundell
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0028
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter focuses on phase transitions, discussing latent heat and deriving the Clausius–Clapeyron equation. It discusses the criteria for stability and metastability, and derives the Gibbs phase ...
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This chapter focuses on phase transitions, discussing latent heat and deriving the Clausius–Clapeyron equation. It discusses the criteria for stability and metastability, and derives the Gibbs phase rule. It introduces colligative properties and classifies the different types of phase transition.Less
This chapter focuses on phase transitions, discussing latent heat and deriving the Clausius–Clapeyron equation. It discusses the criteria for stability and metastability, and derives the Gibbs phase rule. It introduces colligative properties and classifies the different types of phase transition.
M. E. LINES and A. M. GLASS
- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198507789
- eISBN:
- 9780191709944
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507789.003.0010
- Subject:
- Physics, Condensed Matter Physics / Materials
Near the temperature of a second-order structural phase transition, and in particular near the Curie point of a ferroelectric, anomalously strong ultrasonic absorption occurs. This chapter considers ...
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Near the temperature of a second-order structural phase transition, and in particular near the Curie point of a ferroelectric, anomalously strong ultrasonic absorption occurs. This chapter considers the perturbation produced on an acoustic travelling wave by those interactions with a soft optic (ferroelectric) lattice variable. The resulting anomalies affect both the real and imaginary parts of the acoustic frequency and are observable respectively as shifts in acoustic velocity (or equivalently elastic moduli) and in ultrasonic attenuation. In general, the existence of coupling terms, whether in low or high order, leads to characteristic anomalies in other observables which are essentially driven by the primary soft mode. Acoustic anomalies near ferroelectric phase transitions are discussed, including anomalies in sound velocity and elastic constants, along with extrinsic (improper) ferroelectrics and ferroelastics, gadolinium molybdate and its isomorphs, and classification of ferro-materials.Less
Near the temperature of a second-order structural phase transition, and in particular near the Curie point of a ferroelectric, anomalously strong ultrasonic absorption occurs. This chapter considers the perturbation produced on an acoustic travelling wave by those interactions with a soft optic (ferroelectric) lattice variable. The resulting anomalies affect both the real and imaginary parts of the acoustic frequency and are observable respectively as shifts in acoustic velocity (or equivalently elastic moduli) and in ultrasonic attenuation. In general, the existence of coupling terms, whether in low or high order, leads to characteristic anomalies in other observables which are essentially driven by the primary soft mode. Acoustic anomalies near ferroelectric phase transitions are discussed, including anomalies in sound velocity and elastic constants, along with extrinsic (improper) ferroelectrics and ferroelastics, gadolinium molybdate and its isomorphs, and classification of ferro-materials.
Jean Zinn-Justin
- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book provides an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit ...
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This book provides an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, the book emphasizes the role of gaussian distributions and their relations with the mean field approximation and Landau′s theory of critical phenomena. The book shows that quasi-gaussian or mean-field approximations cannot describe correctly phase transitions in three space dimensions. The book assigns this difficulty to the coupling of very different physical length scales, even though the systems we will consider have only local, that is, short range, interactions. To analyze the unusual situation, a new concept is required: the renormalization group, whose fixed points allow understanding the universality of physical properties at large distance, beyond mean-field theory. In the continuum limit, critical phenomena can be described by quantum field theories. In this framework, the renormalization group is directly related to the renormalization process; that is, the necessity to cancel the infinities that arise in straightforward formulations of the theory. The book discusses the renormalization group in the context of various relevant field theories. This leads to proofs of universality and to efficient tools for calculating universal quantities in a perturbative framework. Finally, the book constructs a general functional renormalization group, which can be used when perturbative methods are inadequate.Less
This book provides an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, the book emphasizes the role of gaussian distributions and their relations with the mean field approximation and Landau′s theory of critical phenomena. The book shows that quasi-gaussian or mean-field approximations cannot describe correctly phase transitions in three space dimensions. The book assigns this difficulty to the coupling of very different physical length scales, even though the systems we will consider have only local, that is, short range, interactions. To analyze the unusual situation, a new concept is required: the renormalization group, whose fixed points allow understanding the universality of physical properties at large distance, beyond mean-field theory. In the continuum limit, critical phenomena can be described by quantum field theories. In this framework, the renormalization group is directly related to the renormalization process; that is, the necessity to cancel the infinities that arise in straightforward formulations of the theory. The book discusses the renormalization group in the context of various relevant field theories. This leads to proofs of universality and to efficient tools for calculating universal quantities in a perturbative framework. Finally, the book constructs a general functional renormalization group, which can be used when perturbative methods are inadequate.
Vladimir Dobrosavljevic, Nandini Trivedi, and James M. Valles, Jr. (eds)
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199592593
- eISBN:
- 9780191741050
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199592593.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Quantum phase transitions describe the violent rearrangement of electrons or atoms as they evolve from well defined excitations in one phase to a completely different set of excitations in another. ...
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Quantum phase transitions describe the violent rearrangement of electrons or atoms as they evolve from well defined excitations in one phase to a completely different set of excitations in another. The book chapters give insights into how a coherent metallic or superconducting state can be driven into an incoherent insulating state by increasing disorder, magnetic field, carrier concentration and inter-electron interactions. They illustrate the primary methods employed to develop a multi-faceted theory of many interacting particle systems. They describe how recent experiments probing the microscopic structure, transport, charge and spin dynamics have yielded guiding insights. What sets this book apart is this strong dialog between experiment and theory, which reveals the recent progress and emergent opportunities to solve some major problems in many body physics. The pedagogical style of the chapters has been set for graduate students starting in this dynamic field.Less
Quantum phase transitions describe the violent rearrangement of electrons or atoms as they evolve from well defined excitations in one phase to a completely different set of excitations in another. The book chapters give insights into how a coherent metallic or superconducting state can be driven into an incoherent insulating state by increasing disorder, magnetic field, carrier concentration and inter-electron interactions. They illustrate the primary methods employed to develop a multi-faceted theory of many interacting particle systems. They describe how recent experiments probing the microscopic structure, transport, charge and spin dynamics have yielded guiding insights. What sets this book apart is this strong dialog between experiment and theory, which reveals the recent progress and emergent opportunities to solve some major problems in many body physics. The pedagogical style of the chapters has been set for graduate students starting in this dynamic field.
Marc Mézard and Andrea Montanari
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780198570837
- eISBN:
- 9780191718755
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570837.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and ...
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This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. The topics which have been selected, including spin glasses, error correcting codes, satisfiability, are central to each field. The approach focuses on the limit of large random instances, adopting a common formulation in terms of graphical models. It presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving. It also explains analysis techniques like density evolution and the cavity method, and uses them to derive phase diagrams and study phase transitions.Less
This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. The topics which have been selected, including spin glasses, error correcting codes, satisfiability, are central to each field. The approach focuses on the limit of large random instances, adopting a common formulation in terms of graphical models. It presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving. It also explains analysis techniques like density evolution and the cavity method, and uses them to derive phase diagrams and study phase transitions.
Andrea Braides
- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198507840
- eISBN:
- 9780191709890
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507840.003.0007
- Subject:
- Mathematics, Applied Mathematics
Phase transitions with sharp interfaces are interpreted as segmentation problems, and are approximated with perturbations of non-convex energies (gradient theory of phase transitions). The ...
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Phase transitions with sharp interfaces are interpreted as segmentation problems, and are approximated with perturbations of non-convex energies (gradient theory of phase transitions). The Modica-Mortola theorem is proved, with different formulas characterizing the segmentation energy (optimal-profile problems).Less
Phase transitions with sharp interfaces are interpreted as segmentation problems, and are approximated with perturbations of non-convex energies (gradient theory of phase transitions). The Modica-Mortola theorem is proved, with different formulas characterizing the segmentation energy (optimal-profile problems).
Anatoly Larkin and Andrei Varlamov
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198528159
- eISBN:
- 9780191713521
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528159.003.0016
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter discusses the quantum phase transition using the example of superconductor-insulator transition. For the 3D case, a version of the Ginzburg-Landau formalism is formulated from both ...
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This chapter discusses the quantum phase transition using the example of superconductor-insulator transition. For the 3D case, a version of the Ginzburg-Landau formalism is formulated from both normal and anomalous diffusion. The description of such transition in the case of 2D superconductors is very specific and strongly differs from the 3D case. The ideas of boson and fermion mechanisms of the Tc suppression in 2D cases are presented, and their predictions are compared with the experimental conditions.Less
This chapter discusses the quantum phase transition using the example of superconductor-insulator transition. For the 3D case, a version of the Ginzburg-Landau formalism is formulated from both normal and anomalous diffusion. The description of such transition in the case of 2D superconductors is very specific and strongly differs from the 3D case. The ideas of boson and fermion mechanisms of the Tc suppression in 2D cases are presented, and their predictions are compared with the experimental conditions.
A. J. Leggett
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199211241
- eISBN:
- 9780191706837
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211241.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter argues that the widespread notion that the discipline of condensed matter physics is devoted to deriving the properties of complex many-body systems from that of their atomic-level ...
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This chapter argues that the widespread notion that the discipline of condensed matter physics is devoted to deriving the properties of complex many-body systems from that of their atomic-level components is a myth, and that the analogy of map-making is much more appropriate. After a brief discussion of the experimental techniques available in this area and of the properties of the simplest condensed-matter systems (gases, simple liquids, and crystalline solids), attention is focussed first on the problem of second- and first-order phase transitions, and secondly on issues arising in amorphous (glassy) materials and their possible relevance to biological systems. The chapter concludes by introducing the phenomena of superconductivity and superfluidity, and discussing the general problem of interfacing condensed-matter systems with their environments.Less
This chapter argues that the widespread notion that the discipline of condensed matter physics is devoted to deriving the properties of complex many-body systems from that of their atomic-level components is a myth, and that the analogy of map-making is much more appropriate. After a brief discussion of the experimental techniques available in this area and of the properties of the simplest condensed-matter systems (gases, simple liquids, and crystalline solids), attention is focussed first on the problem of second- and first-order phase transitions, and secondly on issues arising in amorphous (glassy) materials and their possible relevance to biological systems. The chapter concludes by introducing the phenomena of superconductivity and superfluidity, and discussing the general problem of interfacing condensed-matter systems with their environments.
Hidetoshi Nishimori and Gerardo Ortiz
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577224
- eISBN:
- 9780191722943
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577224.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
As an introduction to the physics of phase transitions and critical phenomena, this chapter explains a number of basic and fundamental ideas such as phases, phase transitions, phase diagrams, ...
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As an introduction to the physics of phase transitions and critical phenomena, this chapter explains a number of basic and fundamental ideas such as phases, phase transitions, phase diagrams, universality, and critical phenomena. Especially important is the concept of order parameter, a quantity that measures the degree of asymmetry in the broken symmetry phase. Intuitive accounts are given to the concepts of coarse-graining, and scale and renormalization group transformations, which are powerful, systematic tools to analyze critical behaviour of macroscopic systems. Also explained are several spin and lattice gas model systems, on the basis of which phase transitions and critical phenomena will be studied.Less
As an introduction to the physics of phase transitions and critical phenomena, this chapter explains a number of basic and fundamental ideas such as phases, phase transitions, phase diagrams, universality, and critical phenomena. Especially important is the concept of order parameter, a quantity that measures the degree of asymmetry in the broken symmetry phase. Intuitive accounts are given to the concepts of coarse-graining, and scale and renormalization group transformations, which are powerful, systematic tools to analyze critical behaviour of macroscopic systems. Also explained are several spin and lattice gas model systems, on the basis of which phase transitions and critical phenomena will be studied.
Anatoly Larkin and Andrei Varlamov
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198528159
- eISBN:
- 9780191713521
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528159.003.0012
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter starts off with a discussion of the specifics of superconductivity in ultrasmall superconducting grains. The method of optimal fluctuations in the vicinity of Tc is then introduced, and ...
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This chapter starts off with a discussion of the specifics of superconductivity in ultrasmall superconducting grains. The method of optimal fluctuations in the vicinity of Tc is then introduced, and applied to the study of the formation of superconducting drops in a system with quenched disorder or in strong magnetic fields. The exponential DOS tail in a superconductor with quenched disorder is calculated. Properties of Josephson coupled superconducting grains and drops are discussed. The XY-model for granular superconductor and the GL description of the granular superconductor are formulated. The broadening of superconducting transition by the quenched disorder is found. The final part of the chapter focuses on the specifics of the quantum phase transition in granular superconductors. It discusses Coulomb suppression of superconductivity in the array of tunnel coupled granules, properties of superconducting grains in the normal metal matrix, and phase transition in disordered superconducting film in strong magnetic field.Less
This chapter starts off with a discussion of the specifics of superconductivity in ultrasmall superconducting grains. The method of optimal fluctuations in the vicinity of Tc is then introduced, and applied to the study of the formation of superconducting drops in a system with quenched disorder or in strong magnetic fields. The exponential DOS tail in a superconductor with quenched disorder is calculated. Properties of Josephson coupled superconducting grains and drops are discussed. The XY-model for granular superconductor and the GL description of the granular superconductor are formulated. The broadening of superconducting transition by the quenched disorder is found. The final part of the chapter focuses on the specifics of the quantum phase transition in granular superconductors. It discusses Coulomb suppression of superconductivity in the array of tunnel coupled granules, properties of superconducting grains in the normal metal matrix, and phase transition in disordered superconducting film in strong magnetic field.
Daniel L. Stein and Charles M. Newman
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691147338
- eISBN:
- 9781400845637
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147338.003.0005
- Subject:
- Sociology, Science, Technology and Environment
This chapter finally deals with the concept of spin glasses. The intention is not to provide anything approaching a thorough history of the subject. The field today is broad, with threads and ...
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This chapter finally deals with the concept of spin glasses. The intention is not to provide anything approaching a thorough history of the subject. The field today is broad, with threads and subthreads extending in a multitude of different directions. Rather, the chapter focuses on a relatively narrow part of the overall subject. It discusses some of the history of their discovery, their basic properties and experimental phenomenology, and some of the mysteries surrounding them. It introduces some of the basic theoretical constructs that underlie much of the discussion in later chapters. Topics covered include dilute magnetic alloys and the Kondo effect, nonequilibrium and dynamical behavior, mechanisms underlying spin glass behavior, the Edwards–Anderson Hamiltonian, frustration, dimensionality and phase transitions, broken symmetry and the Edwards–Anderson Order Parameter, and energy landscapes and metastability.Less
This chapter finally deals with the concept of spin glasses. The intention is not to provide anything approaching a thorough history of the subject. The field today is broad, with threads and subthreads extending in a multitude of different directions. Rather, the chapter focuses on a relatively narrow part of the overall subject. It discusses some of the history of their discovery, their basic properties and experimental phenomenology, and some of the mysteries surrounding them. It introduces some of the basic theoretical constructs that underlie much of the discussion in later chapters. Topics covered include dilute magnetic alloys and the Kondo effect, nonequilibrium and dynamical behavior, mechanisms underlying spin glass behavior, the Edwards–Anderson Hamiltonian, frustration, dimensionality and phase transitions, broken symmetry and the Edwards–Anderson Order Parameter, and energy landscapes and metastability.
