| Preface | p. xvii |
| Preface to the Third Edition | p. xix |
| General Sources and References | p. xxiii |
| Basic Ideas and Techniques | |
| Pertinent concepts and ideas in the theory of critical phenomena | p. 3 |
| Description of critical phenomena | p. 3 |
| Scaling and homogeneity | p. 5 |
| Comparison of various results for critical exponents | p. 6 |
| Universality - dimensionality, symmetry | p. 8 |
| Exercises | p. 9 |
| Formulation of the problem of phase transitions in terms of functional integrals | p. 11 |
| Introduction | p. 11 |
| Construction of the Lagrangian | p. 12 |
| The parameters appearing in L | p. 14 |
| The partition function, or the generating functional | p. 15 |
| Representation of the Ising model in terms of functional integrals | p. 18 |
| Correlation functions including composite operators | p. 28 |
| Exercises | p. 30 |
| Functional integrals in quantum field theory | p. 33 |
| Introduction | p. 33 |
| Functional integrals for a quantum-mechanical system with one degree of freedom | p. 34 |
| Functional integrals for the scalar boson field theory | p. 41 |
| Exercises | p. 50 |
| Perturbation theory and Feynman graphs | p. 53 |
| Introduction | p. 53 |
| Perturbation expansion in coordinate space | p. 54 |
| The cancellation of vacuum graphs | p. 60 |
| Rules for the computation of graphs | p. 60 |
| More general cases | p. 63 |
| Diagrammatic expansion in momentum space | p. 68 |
| Perturbation expansion of Green functions with composite operators | p. 72 |
| Exercises | p. 77 |
| Vertex functions and symmetry breaking | p. 80 |
| Introduction | p. 80 |
| Connected Green functions and their generating functional | p. 82 |
| The mass operator | p. 85 |
| The Legendre transform and vertex functions | p. 86 |
| The generating functional and the potential | p. 91 |
| Ward-Takahashi identities and Goldstone's theorem | p. 94 |
| Vertex parts for Green functions with composite operators | p. 96 |
| Exercises | p. 101 |
| Expansions in the number of loops and in the number of components | p. 103 |
| Introduction | p. 103 |
| The expansion in the number of loops as a power series | p. 104 |
| The tree (Landau-Ginzburg) approximation | p. 105 |
| The one-loop approximation and the Ginzburg criterion | p. 109 |
| Mass and coupling constant renormalization in the one-loop approximation | p. 112 |
| Composite field renormalization | p. 116 |
| Renormalization of the field at the two-loop level | p. 117 |
| The 0(M)-symmetric theory in the limit of large M | p. 126 |
| The method of steepest descent and the loop expansion | p. 137 |
| Exercises | p. 142 |
| Renormalization | p. 147 |
| Introduction | p. 147 |
| Some considerations concerning engineering dimensions | p. 148 |
| Power counting and primitive divergences | p. 151 |
| Renormalization of a cutoff o[superscript 4] theory | p. 157 |
| Normalization conditions for massive and massless theories | p. 159 |
| Renormalization constants for a massless theory to order two loops | p. 161 |
| Renormalization away from the critical point | p. 164 |
| Counterterms | p. 167 |
| Relevant and irrelevant operators | p. 169 |
| Renormalization of a o[superscript 4] theory with an 0(M) symmetry | p. 171 |
| Ward identities and renormalization | p. 174 |
| Iterative construction of counterterms | p. 179 |
| Exercises | p. 185 |
| The renormalization group and scaling in the critical region | p. 189 |
| Introduction | p. 189 |
| The renormalization group for the critical (massless) theory | p. 190 |
| Regularization by continuation in the number of dimensions | p. 195 |
| Massless theory below four dimensions - the emergence of [epsilon] | p. 196 |
| The solution of the renormalization group equation | p. 197 |
| Fixed points, scaling, and anomalous dimensions | p. 199 |
| The approach to the fixed point - asymptotic freedom | p. 201 |
| Renormalization group equation above T[subscript c]-identification of v | p. 205 |
| Below the critical temperature - the scaling form of the equation of state | p. 208 |
| The specific heat - renormalization group equation for an additively renormalized vertex | p. 210 |
| The Callan-Symanzik equations | p. 212 |
| Renormalization group equations for the bare theory | p. 214 |
| Renormalization group equations and scaling in the infinite M limit | p. 217 |
| General formulas for calculating Feynman integrals | p. 222 |
| Exercises | p. 223 |
| The computation of the critical exponents | p. 228 |
| Introduction | p. 228 |
| The symbolic calculation of the renormalization constants and Wilson functions | p. 230 |
| The [epsilon] expansion of the critical exponents | p. 233 |
| The nature of the fixed points - universality | p. 237 |
| Scale invariance at finite cutoff | p. 238 |
| At the critical dimension - asymptotic infrared freedom | p. 240 |
| [epsilon] expansion for the Callan-Symanzik method | p. 243 |
| [epsilon] expansion of the renormalization group equations for the bare functions | p. 247 |
| Dimensional regularization and critical phenomena | p. 248 |
| Renormalization by minimal subtraction of dimensional poles | p. 250 |
| The calculation of exponents in minimal subtraction | p. 255 |
| Calculation of some integrals with cutoff | p. 257 |
| One-loop integrals in dimensional regularization | p. 260 |
| Two-loop integrals in dimensional regularization | p. 263 |
| Exercises | p. 266 |
| Further Applications and Developments | |
| Introduction | p. 273 |
| Beyond leading scaling | p. 275 |
| Corrections to scaling in a o[superscript 4] theory | p. 275 |
| Finite-size scaling | p. 277 |
| Anomalous dimensions of high composite operators | p. 280 |
| Corrections due to irrelevant operators | p. 288 |
| Next-to-leading terms in the scaling region | p. 293 |
| The operator product expansion | p. 295 |
| Computation of next-to-leading terms in [epsilon]-expansion | p. 297 |
| Renormalized equations of motion | p. 300 |
| Exercises | p. 306 |
| Universality revisited | p. 310 |
| Renormalization scheme independence of critical exponents | p. 310 |
| The universal form of the equation of state | p. 311 |
| The equation of state to order [epsilon] | p. 314 |
| Two scale factor universality - universal ratios of amplitudes | p. 316 |
| Exercises | p. 320 |
| Critical behavior with several couplings | p. 323 |
| Introduction | p. 323 |
| More than one coupling constant - cubic anisotropy | p. 324 |
| Runaway trajectories | p. 328 |
| First order transitions induced by fluctuations: the Coleman-Weinberg mechanism | p. 330 |
| Geometrical description of the Coleman-Weinberg phenomenon | p. 337 |
| Exercises | p. 339 |
| Crossover phenomena | p. 342 |
| Introduction | p. 342 |
| Crossover in magnetic systems interacting quadratically and the Harris criterion for relevance of random dilution | p. 343 |
| The crossover exponent at a bicritical point: scale invariance with quadratic symmetry breaking | p. 346 |
| The crossover function at a bicritical point: a case study of renormalization group analysis in the presence of two lengths | p. 350 |
| Exercises | p. 361 |
| Critical phenomena near two dimensions | p. 364 |
| An alternative field theory for the Heisenberg model - the low temperature phase | p. 364 |
| Perturbation theory for the non-linear sigma model | p. 368 |
| Renormalization group treatment of the non-linear sigma model | p. 372 |
| Scaling behavior and critical exponents | p. 376 |
| Renormalization of the non-linear sigma model | p. 378 |
| Exercises | p. 380 |
| Nonperturbative and Numerical Methods | |
| Real space methods | p. 385 |
| Introduction | p. 385 |
| Real space renormalization group | p. 395 |
| At and around a fixed point | p. 414 |
| The large M model | p. 427 |
| Exercises | p. 439 |
| Finite size scaling | p. 446 |
| Introduction | p. 446 |
| The RG derivation of finite size scaling | p. 456 |
| Applications of FSS | p. 470 |
| Exercises | p. 480 |
| Monte Carlo methods. Numerical field theory | p. 486 |
| Introduction | p. 486 |
| Dynamic Monte Carlo | p. 492 |
| Data analysis | p. 499 |
| Cluster methods | p. 509 |
| Exercises | p. 516 |
| Appendix A Sample Programs | |
| Static Monte Carlo Integration | |
| Simulation of 2-D Ising Model | |
| Autocorrelation Analysis | |
| Data Analysis | p. 521 |
| Author Index | p. 521 |
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