Modern Theory of Critical Phenomena [electronic resource]

An important contributor to our current understanding of critical phenomena, Ma introduces the beginner--especially the graduate student with no previous knowledge of the subject-to fundamental theoretical concepts such as mean field theory, the scaling hypothesis, and the renormalization group. He...

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Bibliographic Details
Online Access:	Full Text (via Taylor & Francis)
Main Author:	Ma, Shang-Keng
Format:	Electronic eBook
Language:	English
Published:	Boulder : Routledge, 2018.
Series:	Advanced Books Classics.
Subjects:	Critical phenomena (Physics)

Table of Contents:

Chapter SUMMARY
chapter 2 QUALITATIVE PICTURE
chapter 3 THERMODYNAMIC PROPERTIES AND EXPONENTS
chapter 4 FLUCTUATIONS OF THE ORDER PARAMETER, SCATTERING EXPERIMENTS, THE EXPONENT ?
chapter 5 OBSERVATIONS ON OTHER KINDS OF CRITICAL POINTS
chapter 6 SUMMARY OF QUALITATIVE FEATURES OF STATIC PHENOMENA
chapter 7 MEAN FIELD THEORY
chapter SUMMARY
chapter 2 CLASSICAL MODELS OF THE CELL HAMILTONIAN
chapter 3 STATISTICAL MECHANICS
chapter 4 BLOCK HAMILTONIANS AND KADANOFF TRANSFORMATIONS
chapter 5 GINZBURG-LANDAU FORM
chapter SUMMARY
chapter 1 MOST PROBABLE VALUE AND GAUSSIAN APPROXIMATION
chapter 2 MINIMUM OF THE GINZBURG-LANDAU HAMILTONIAN, LANDAU THEORY
chapter 3 GAUSSIAN APPROXIMATION FOR T > Tc
chapter 4 GAUSSIAN APPROXIMATION FOR T < Tc
chapter 5 THE CORRELATION LENGTH AND TEMPERATURE DEPENDENCE
chapter 6 SUMMARY OF RESULTS AND THE GINZBURG CRITERION
chapter 7 FLUCTUATION AND DIMENSION
chapter 8 DISCUSSION
chapter SUMMARY
chapter 2 SCALE TRANSFORMATION AND DIMENSIONAL ANALYSIS
chapter 3 DISCUSSION
chapter SUMMARY
chapter 2 DEFINITION OF THE RENORMALIZATION GROUP (RG)
chapter 3 ALTERNATIVES IN DEFINING THE RG
chapter 4 CONCLUDING REMARK
chapter SUMMARY
chapter 1 THE FIXED POINT AND ITS NEIGHBORHOOD
chapter 2 LARGE s BEHAVIOR OF Rs AND CRITICAL EXPONENTS
chapter 3 THE FREE ENERGY
chapter 4 CRITICAL REGION
chapter 5 SUMMARY AND REMARKS
chapter SUMMARY
chapter 1 THE GAUSSIAN FIXED POINT
chapter 2 THE LINEARIZED RG NEAR THE GAUSSIAN FIXED POINT
chapter 3 RELEVANT, IRRELEVANT, AND MARGINAL PARAMETERS, SCALING FIELDS, AND CROSSOVER
chapter 4 CRITICAL EXPONENTS FOR d > 4
chapter 5 THE RG FOR d 4
? AND FIXED POINTS TO O(?)
chapter 6 EFFECT OF OTHER O(?2) TERMS IN Rs?
chapter SUMMARY
chapter 1 THE RG IN THE LARGE-n LIMIT
chapter 2 WILSON'S RECURSION FORMULA
chapter 3 APPLICATION TO THE n → ∞
chapter 4 DEFINITIONS OF THE RG FOR DISCRETE SPINS
chapter 5 NUMERICAL WORK ON THE RG FOR TWO-DIMENSIONAL ISING SYSTEMS
chapter 6 DISCUSSION
chapter SUMMARY
chapter 1 USE OF PERTURBATION THEORY IN STUDYING CRITICAL PHENOMENA
chapter 2 PERTURBATION EXPANSION OF THE GINZBURG-LANDAU MODEL
chapter 3 DIVERGENCE OF THE PERTURBATION EXPANSION AT THE CRITICAL POINT
chapter 4 THE 1/n EXPANSION OF CRITICAL EXPONENTS
chapter 5 THE ? EXPANSION OF CRITICAL EXPONENTS
chapter 6 SIMPLE ILLUSTRATIVE CALCULATIONS, ? AND ?
chapter 7 THE PERTURBATION EXPANSION IN THE PRESENCE OF A NONZERO ( ? )
chapter 8 REMARKS
chapter 9 THE RG IN THE PERTURBATION EXPANSION
chapter 10 ANISOTROPIC PARAMETERS AND COMMENTS. ON THE LIQUID-GAS CRITICAL POINT
chapter 11 TABLES OF EXPONENTS IN ? AND 1/n EXPANSIONS
chapter SUMMARY
chapter 2 THE RG APPROACH TO NONMAGNETIC IMPURITIES
chapter 3 FIXED POINT STABILITY CRITERIA AND OTHER IMPURITIES
chapter 4 COMMENTS ON GRAPHS
chapter 5 THE SELF-AVOIDING RANDOM WALK PROBLEM
chapter 6 OTHER NON-IDEAL FEATURES OF REAL SYSTEMS
chapter SUMMARY
chapter 2 BROWNIAN MOTION AND KINETIC EQUATIONS
chapter 3 RELAXATION TIMES
chapter 4 ELIMINATION OF FAST MODES
chapter 5 RESPONSE FUNCTIONS AND CORRELATION FUNCTIONS
chapter 6 THE VAN HOVE THEORY
chapter SUMMARY
chapter 2 TRANSFORMATION OF CORRELATION FUNCTIONS AND RESPONSE FUNCTIONS
chapter 3 FIXED POINTS, CRITICAL BEHAVIOR, AND DYNAMIC SCALING
chapter SUMMARY
chapter 1 THE TIME-DEPENDENT GINZBURG-LANDAU MODELS (TDGL)
chapter 2 EFFECTS OF SLOW HEAT CONDUCTION
chapter 3 THE ISOTROPIC FERROMAGNET
chapter 4 UNIVERSALITY IN CRITICAL DYNAMICS
chapter SUMMARY
chapter 2 REPRESENTATION OF TERMS BY GRAPHS, RULES OF CALCULATION
chapter 3 THE FLUCTUATION-DISSIPATION THEOREM
chapter 4 GRAPHS FOR HIGHER RESPONSE AND CORRELATION FUNCTIONS
chapter 5 ADDITIONAL MODES AND MODE-MODE COUPLING TERMS
chapter 1 AN ALTERNATIVE FORMULATION OF COARSE GRAINING, THE CLASSICAL FIELD CONFIGURATIONS
chapter 2 SMOOTH CUTOFF.
3. DISCUSSIONV. THE RENORMALIZATION GROUP; SUMMARY; 1. MOTIVATION; 2. DEFINITION OF THE RENORMALIZATION GROUP (RG); 3. ALTERNATIVES IN DEFINING THE RG; 4. CONCLUDING REMARK; VI. FIXED POINTS AND EXPONENTS; SUMMARY; 1. THE FIXED POINT AND ITS NEIGHBORHOOD; 2. LARGE s BEHAVIOR OF Rs AND CRITICAL EXPONENTS; 3. THE FREE ENERGY; 4. CRITICAL REGION; 5. SUMMARY AND REMARKS; VII. THE GAUSSIAN FIXED POINT AND FIXED POINTS IN 4
ε DIMENSIONS; SUMMARY; 1. THE GAUSSIAN FIXED POINT; 2. THE LINEARIZED RG NEAR THE GAUSSIAN FIXED POINT
3. RELEVANT, IRRELEVANT, AND MARGINAL PARAMETERS, SCALING FIELDS, AND CROSSOVER4. CRITICAL EXPONENTS FOR d> 4; 5. THE RG FOR d = 4
ε AND FIXED POINTS TO O(ε); 6. EFFECT OF OTHER O(ε2) TERMS IN Rsμ; VIII. RENORMALIZATION GROUPS IN SELECTED MODELS; SUMMARY; 1. THE RG IN THE LARGE-n LIMIT; 2. WILSON'S RECURSION FORMULA; 3. APPLICATION TO THE n → ∞; 4. DEFINITIONS OF THE RG FOR DISCRETE SPINS; 5. NUMERICAL WORK ON THE RG FOR TWO-DIMENSIONAL ISING SYSTEMS; 6. DISCUSSION; IX. PERTURBATION EXPANSIONS; SUMMARY; 1. USE OF PERTURBATION THEORY IN STUDYING CRITICAL PHENOMENA
Cover; Half Title; Title; Copyright; Dedication; CONTENTS; Editor's Foreword; PREFACE; I. INTRODUCTION; SUMMARY; 1. CRITICAL POINTS AND ORDER PARAMETERS; 2. QUALITATIVE PICTURE; 3. THERMODYNAMIC PROPERTIES AND EXPONENTS; 4. FLUCTUATIONS OF THE ORDER PARAMETER, SCATTERING EXPERIMENTS, THE EXPONENT η; 5. OBSERVATIONS ON OTHER KINDS OF CRITICAL POINTS; 6. SUMMARY OF QUALITATIVE FEATURES OF STATIC PHENOMENA; 7. MEAN FIELD THEORY; II. MODELS AND BASIC CONCEPTS; SUMMARY; 1. SEQUENCE OF MODELS; 2. CLASSICAL MODELS OF THE CELL HAMILTONIAN; 3. STATISTICAL MECHANICS
2. PERTURBATION EXPANSION OF THE GINZBURG-LANDAU MODEL3. DIVERGENCE OF THE PERTURBATION EXPANSION AT THE CRITICAL POINT; 4. THE 1/n EXPANSION OF CRITICAL EXPONENTS; 5. THE ε EXPANSION OF CRITICAL EXPONENTS; 6. SIMPLE ILLUSTRATIVE CALCULATIONS, η AND α; 7. THE PERTURBATION EXPANSION IN THE PRESENCE OF A NONZERO (σ); 8. REMARKS; 9. THE RG IN THE PERTURBATION EXPANSION; 10. ANISOTROPIC PARAMETERS AND COMMENTS. ON THE LIQUID-GAS CRITICAL POINT; 11. TABLES OF EXPONENTS IN ε AND 1/n EXPANSIONS; X. THE EFFECT OF RANDOM IMPURITIES AND MISCELLANEOUS TOPICS; SUMMARY; 1. RANDOM IMPURITIES

Modern Theory of Critical Phenomena [electronic resource]

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