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Elements of Phase Transitions and Critical Phenomena

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


The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence

Robert W. Batterman

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195146479
eISBN:
9780199833078
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0195146476.001.0001
Subject:
Philosophy, Philosophy of Science

This book focuses on a form of reasoning in science that I call “asymptotic reasoning.” At base, this type of reasoning involves methods that eliminate details and, in some sense, precision. ... More


Conclusions and Outlook

M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko

in Advances in the Casimir Effect

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199238743
eISBN:
9780191716461
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238743.003.0025
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter contains conclusions and some words about the outlook. The main conclusion is that at present there is already very good agreement between the theory, adapted for the case of real ... More


Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing: Lecture Notes of the Les Houches Summer School: Volume 93, August 2009

Laurent Lellouch, Rainer Sommer, Benjamin Svetitsky, Anastassios Vladikas, and Leticia F. Cugliandolo (eds)

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199691609
eISBN:
9780191731792
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199691609.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The book is based on the lectures delivered at the XCIII Session of the ´Ecole de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of Ph.D. ... 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


Principles of systematic upscaling

Achi Brandt

in Multiscale Methods: Bridging the Scales in Science and Engineering

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199233854
eISBN:
9780191715532
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233854.003.0007
Subject:
Mathematics, Applied Mathematics

Building on the complementary advantages of Renormalization Group (RG) and multigrid (MG) methods, Systematic Upscaling (SU) comprises rigorous procedures for deriving suitable variables and ... More


The Theory Of QCD

GÜNTHER DISSERTORI, IAN G. KNOWLES, and MICHAEL SCHMELLING

in Quantum Chromodynamics: High Energy Experiments and Theory

Published in print:
2009
Published Online:
January 2010
ISBN:
9780199566419
eISBN:
9780191708060
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566419.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter begins with the formal derivation of QCD as a gauge theory based on the symmetry group SU(3). It then describes the basic reactions of lepton-lepton, lepton-hadron, and hadron-hadron ... More


Mass renormalization in nonrelativistic quantum electrodynamics

Volker Bach

in Quantum Theory from Small to Large Scales: Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199652495
eISBN:
9780191741203
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652495.003.0008
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter contains an overview on recent results related to the mass renormalization in nonrelativistic quantum electrodynamics. Following this overview, the construction of the renormalization ... More


HOLOMORPHY

John Terning

in Modern Supersymmetry: Dynamics and Duality

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567639
eISBN:
9780191718243
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567639.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Two of the early exciting observations about ☐ = 1 SUSY gauge theories were the absence of quadratic loop corrections to scalar masses and the absence of renormalization for many superpotentials. ... More


BEYOND MEAN-FIELD THEORY

Glenn H. Fredrickson

in The Equilibrium Theory of Inhomogeneous Polymers

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567295
eISBN:
9780191717956
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567295.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes analytical and numerical methods for analyzing polymer field theory models beyond the mean-field approximation. Analytical treatments of field fluctuations at the Gaussian ... More


BOSONIZATION

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter explains bosonization, a useful technique for describing the low-energy properties of one-dimensional systems. Bosonization is introduced by presenting a model on which this method is ... More


FLUCTUATION THERMODYNAMICS

Anatoly Larkin and Andrei Varlamov

in Theory of Fluctuations in Superconductors

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528159
eISBN:
9780191713521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528159.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the Ginzburg-Landau functional and provides a general description of fluctuation thermodynamics within the framework of the functional integration over the fluctuation fields ... More


MICROSCOPIC THEORY OF FLUCTUATION CONDUCTIVITY

Anatoly Larkin and Andrei Varlamov

in Theory of Fluctuations in Superconductors

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528159
eISBN:
9780191713521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528159.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents a microscopic analysis of the different fluctuation contributions to the conductivity tensor. The physical origin and a qualitative evaluation of Aslamazov-Larkin, ... More


DOS AND TUNNELING

Anatoly Larkin and Andrei Varlamov

in Theory of Fluctuations in Superconductors

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528159
eISBN:
9780191713521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528159.003.0009
Subject:
Physics, Condensed Matter Physics / Materials

The chapter starts with a discussion of the density of states renormalization in the normal state of a superconductor caused by fluctuation pairing which occurs close to the transition temperature. ... More


GENESIS OF QUANTUM ANOMALIES

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews the history of quantum anomalies. The original indication of the anomaly appeared immediately after the modern formulation of field theory, namely, renormalization theory. ... More


THE WEYL ANOMALY AND RENORMALIZATION GROUP

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the quantum anomaly associated with the scale transformation of space-time coordinates, or the transformation generally called the Weyl transformation. In flat space-time, this ... More


From Random Walks to Random Matrices

Jean Zinn-Justin

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models ... More


Phase transitions and critical phenomena

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/9780199577224.003.0001
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, ... More


Implementation of the renormalization group

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/9780199577224.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Actual computations of fixed points and eigenvalues usually involve approximations, often crude ones, except for a very limited number of simple cases such as the one-dimensional Ising model of the ... More


Asymptotic Explanation

Robert W. Batterman

in The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195146479
eISBN:
9780199833078
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195146476.003.0004
Subject:
Philosophy, Philosophy of Science

This chapter provides a fairly detailed discussion of the renormalization group account of the universality of critical phenomena. This discussion allows one to determine the distinctive features of ... More


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