Modern theory of critical phenomena

CONTENTS......Page 10
PREFACE......Page 18
1. CRITICAL, POINTS AND ORDER PARAMETERS......Page 28
2. QUALITATIVE PICTURE......Page 32
3. THERMODYNAMIC PROPERTIES AND EXPONENTS......Page 37
4. FLUCTUATIONS OF THE ORDER PARAMETER, SCATTERING EXPERIMENTS, THE EXPONENT......Page 43
5. OBSERVATIONS ON OTHER KINDS OF CRITICAL POINTS......Page 48
6. SUMMARY OF QUALITATIVE FEATURES OF STATIC PHENOMENA......Page 59
7. MEAN FIELD THEORY......Page 61
1. SEQUENCE OF MODELS......Page 67
2. CLASSICAL MODELS OF THE CELL HAMILTONIAN......Page 72
3. STATISTICAL MECHANICS......Page 77
4. BLOCK HAMILTONIANS AND KADANOFF TRANSFORMATIONS......Page 83
5. GINZBURG-LANDAU FORM......Page 94
SUMMARY......Page 99
1. MOST PROBABLE VALUE AND GAUSSIAN APPROXIMATION......Page 100
2. MINIMUM OF THE GINZBURG­LANDAU HAMILTONIAN, LANDAU THEORY......Page 103
3. GAUSSIAN APPROXIMATION FOR T > T[sub(c)]......Page 109
4. GAUSSIAN APPROXIMATION FOR T < T[sub(c)]......Page 113
5. THE CORRELATION LENGTH AND TEMPERATURE DEPENDENCE......Page 116
6. SUMMARY OF RESULTS AND THE GINZBURG CRITERION......Page 119
7. FLUCTUATION AND DIMENSION......Page 123
8. DISCUSSION......Page 127
1. THE CORRELATION LENGTH AND THE SCALING HYPOTHESIS......Page 130
2. SCALE TRANSFORMATION AND DIMENSIONAL ANALYSIS......Page 135
3. DISCUSSION......Page 141
1. MOTIVATION......Page 143
2. DEFINITION OF THE RENORMALIZATION GROUP (RG)......Page 146
3. ALTERNATIVES IN DEFINING THE RG......Page 156
4. CONCLUDING REMARK......Page 160
SUMMARY......Page 161
1. THE FIXED POINT AND ITS NEIGHBORHOOD......Page 162
2. LARGE s BEHAVIOR OF R[sub(s)] AND CRITICAL EXPONENTS......Page 166
3. THE FREE ENERGY......Page 176
4. CRITICAL REGION......Page 184
5. SUMMARY AND REMARKS......Page 186
SUMMARY......Page 190
1. THE GAUSSIAN FIXED POINT......Page 191
2. THE LINEARIZED RG NEAR THE GAUSSIAN FIXED POINT......Page 196
3. RELEVANT, IRRELEVANT, AND MARGINAL PARAMETERS, SCALING FIELDS, AND CROSSOVER......Page 206
4. CRITICAL EXPONENTS FOR d > 4......Page 212
5. THE RG FOR d = 4 - ε AND FIXED POINTS TO O(ε)......Page 215
6. EFFECT OF OTHER O(ε[sup(2)]) TERMS IN R[sub(S)]μ......Page 234
SUMMARY......Page 246
1. THE RG IN THE LARGE-n LIMIT......Page 247
2. WILSON\'S RECURSION FORMULA......Page 256
3. APPLICATION TO THE n → ∞......Page 267
4. DEFINITIONS OF THE RG FOR DISCRETE SPINS......Page 271
5. NUMERICAL WORK ON THE RG FOR TWO-DIMENSIONAL ISING SYSTEMS......Page 287
6. DISCUSSION......Page 298
SUMMARY......Page 304
1. USE OF PERTURBATION THEORY IN STUDYING CRITICAL PHENOMENA......Page 305
2. PERTURBATION EXPANSION OF THE GINZBURG-LANDAU MODEL......Page 307
3. DIVERGENCE OF THE PERTURBATION EXPANSION AT THE CRITICAL POINT......Page 325
4. THE 1/n EXPANSION OF CRITICAL EXPONENTS......Page 328
5. THE ε EXPANSION OF CRITICAL EXPONENTS......Page 336
6. SIMPLE ILLUSTRATIVE CALCULATIONS, η AND α......Page 341
7. THE PERTURBATION EXPANSION IN THE PRESENCE OF A NONZERO <σ>......Page 351
8. REMARKS......Page 363
9. THE RG IN THE PERTURBATION EXPANSION......Page 366
10. ANISOTROPIC PARAMETERS AND COMMENTS ON THE LIQUID-GAS CRITICAL POINT......Page 373
11. TABLES OF EXPONENTS IN ε AND 1/n EXPANSIONS......Page 381
1. RANDOM IMPURITIES......Page 386
2. THE RG APPROACH TO NONMAGNETIC IMPURITIES......Page 397
3. FIXED POINT STABILITY CRITERIA AND OTHER IMPURITIES......Page 409
4. COMMENTS ON GRAPHS......Page 417
5. THE SELF-AVOIDING RANDOM WALK PROBLEM......Page 427
6. OTHER NON-IDEAL FEATURES OF REAL SYSTEMS......Page 441
1. INTRODUCTION......Page 447
2. BROWNIAN MOTION AND KINETIC EQUATIONS......Page 452
3. RELAXATION TIMES......Page 459
4. ELIMINATION OF FAST MODES......Page 462
5. RESPONSE FUNCTIONS AND CORRELATION FUNCTIONS......Page 466
6. THE VAN HOVE THEORY......Page 469
1. THE TIME-DEPENDENT GINZBURGLANDAU MODELS (TDGL)......Page 477
2. TRANSFORMATION OF CORRELATION FUNCTIONS AND RESPONSE FUNCTIONS......Page 481
3. FIXED POINTS, CRITICAL BEHAVIOR, AND DYNAMIC SCALING......Page 485
2. EFFECTS OF SLOW HEAT CONDUCTION......Page 499
3. THE ISOTROPIC FERROMAGNET......Page 515
4. UNIVERSALITY IN CRITICAL DYNAMICS......Page 521
1. ITERATION SOLUTION OF KINETIC EQUATIONS......Page 525
2. REPRESENTATION OF TERMS BY GRAPHS, RULES OF CALCULATION......Page 528
3. THE FLUCTUATION-DISSIPATION THEOREM......Page 537
4. GRAPHS FOR HIGHER RESPONSE AND CORRELATION FUNCTIONS......Page 543
5. ADDITIONAL MODES AND MODE-MODE COUPLING TERMS......Page 547
1. AN ALTERNATIVE FORMULATION OF COARSE GRAINING, THE CLASSICAL FIELD CONFIGURATIONS......Page 555
2. SMOOTH CUTOFF......Page 562
REFERENCES......Page 569
C......Page 582
D......Page 583
G......Page 584
L......Page 585
P......Page 586
S......Page 587
W......Page 588