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Mean‐field theories

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The present chapter explains the mean-field approximation, the Landau theory, the infinite-range model, and the Bethe approximation, and shows that all these (mean-field) theories are essentially ... More


Renormalization group and scaling

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Mean-field theory is usually taken as a first step toward understanding critical phenomena, providing an overview that reveals qualitative behaviour of physical quantities. However, it is necessary ... More


Critical phenomena and scaling theory

Barry M. McCoy

in Advanced Statistical Mechanics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199556632
eISBN:
9780191723278
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556632.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the phenomenological description of critical phenomena. It derives inequalities for critical exponents which follow from thermodynamics. It explains the scaling theory of ... More


High temperature expansions for magnets at H = 0

Barry M. McCoy

in Advanced Statistical Mechanics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199556632
eISBN:
9780191723278
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556632.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the results of high temperature series expansions for classical n component spin models with nearest neighbor interactions for two and three dimensions. In dimension three this ... More


Spontaneous time‐symmetry breaking in a vibrating cold atom system

M.-S. Heo, Y. Kim, H.-R. Noh, and W. Jhe

in Fluctuating Nonlinear Oscillators: From Nanomechanics to Quantum Superconducting Circuits

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199691388
eISBN:
9780191742255
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199691388.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter describes the experimental and theoretical studies of a spontaneous time-translation symmetry breaking transition in a non-equilibrium cold atom system. Such studies prepare two ... More


Thermodynamic Scaling Near the Critical Point

Eldred H. Chimowitz

in Introduction to Critical Phenomena in Fluids

Published in print:
2005
Published Online:
November 2020
ISBN:
9780195119305
eISBN:
9780197561249
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195119305.003.0005
Subject:
Chemistry, Physical Chemistry

Thermodynamic scaling near the critical point is a signature of critical phenomena, and many useful applications of supercritical solvent fluids depend upon exploiting this behavior in some ... More


Quantum phase transitions

G. G. Batrouni and R. T. Scalettar

in Ultracold Gases and Quantum Information: Lecture Notes of the Les Houches Summer School in Singapore: Volume 91, July 2009

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199603657
eISBN:
9780191729515
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199603657.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses quantum phase transitions (QPT). It starts with a brief review of thermal phase transitions, critical exponents and scaling laws. The scaling laws are then generalized to the ... More


Field theory: Perturbative expansion and summation methods

Jean Zinn-Justin

in From Random Walks to Random Matrices

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.003.0023
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 23 examines perturbative expansion and summation methods in field theory. In quantum field theory, all perturbative expansions are divergent series in the mathematical sense. This leads to a ... More


Renormalization Group: From a general concept to numbers

Jean Zinn-Justin

in From Random Walks to Random Matrices

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 5 first recalls the importance of the concept of scale decoupling in physics. It then emphasizes that quantum field theory and the theory of critical phenomena have provided two examples ... More


Continuous phase transitions

Andrew M. Steane

in Thermodynamics: A complete undergraduate course

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198788560
eISBN:
9780191830426
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198788560.003.0025
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The general phenomenon of continuous phase transitions is discussed, and treated by the Landau mean field approach. First some illustrative examples are discussed, and the concepts of order parameter ... More


Phase Transitions and the Ising Model

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198853237
eISBN:
9780191887703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853237.003.0031
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

Chapter 17 presented one example of a phase transition, the van der Waals gas. This chapter provides another, the Ising model, a widely studied model of phase transitions. We first give the solution ... More


Critical exponents and equation of state from series summation

Jean Zinn-Justin

in Quantum Field Theory and Critical Phenomena: Fifth Edition

Published in print:
2021
Published Online:
June 2021
ISBN:
9780198834625
eISBN:
9780191872723
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198834625.003.0041
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Universal quantities near the phase transition of O(N) symmetric vector models, can be determined, in the framework of the (f2 )2 field theory, and the corresponding renormalization group (RG), in ... More


Ferromagnetism: a renormalization group tutorial

Tom Lancaster and Stephen J. Blundell

in Quantum Field Theory for the Gifted Amateur

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199699322
eISBN:
9780191779435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199699322.003.0036
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter treats the ferromagnetic transition as a further example of the renormalization group procedure and shows how critical exponents can be extracted.


Magnetic Materials: From Isolated Moments to Ordered Arrangements

Kannan M. Krishnan

in Fundamentals and Applications of Magnetic Materials

Published in print:
2016
Published Online:
December 2016
ISBN:
9780199570447
eISBN:
9780191813504
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570447.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

The magnetic behavior of materials can be quite diverse with a wide range of susceptibilities. All materials exhibit diamagnetism with a very small, negative susceptibility and it is predominant in ... More


Quantum Field Theory and Critical Phenomena: Fifth Edition

Jean Zinn-Justin

Published in print:
2021
Published Online:
June 2021
ISBN:
9780198834625
eISBN:
9780191872723
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198834625.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamic (QED) has been the first example of a quantum field theory (QFT). Eventually, QFT has become the framework for ... More


The Phase Transition in the Random HornSAT Problem

Demetrios D. Demopoulos and Moshe Y. Vardi

in Computational Complexity and Statistical Physics

Published in print:
2005
Published Online:
November 2020
ISBN:
9780195177374
eISBN:
9780197562260
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195177374.003.0017
Subject:
Computer Science, Mathematical Theory of Computation

This chapter presents a study of the satisfiability of random Horn formulas and a search for a phase transition. In the past decade, phase transitions or sharp thresholds, have been studied ... More


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