| Contents of Volume 2 | p. ix |
| Preface | p. xi |
| From Brownian motion to Euclidean fields | p. 1 |
| Brownian motion | p. 1 |
| Random walks | p. 1 |
| The sum over paths | p. 9 |
| The dimension two of Brownian curves | p. 12 |
| Euclidean fields | p. 21 |
| Free fields | p. 22 |
| Interacting fields and random walks | p. 25 |
| Self-avoiding walks and the limit n [right arrow] 0 | p. 31 |
| Comparison with the high temperature expansion | p. 33 |
| The one-dimensional case | p. 37 |
| Lattices | p. 43 |
| Notes | p. 47 |
| Grassmannian integrals and the two-dimensional Ising model | p. 48 |
| Grassmannian integrals | p. 48 |
| Anticommuting variables | p. 48 |
| Integrals | p. 52 |
| The two-dimensional Ising model | p. 58 |
| Duality | p. 59 |
| Transfer matrix | p. 62 |
| Fermionic representation | p. 63 |
| Free energy | p. 67 |
| Spontaneous magnetization | p. 72 |
| Correlation function in the high temperature phase | p. 78 |
| Surface tension | p. 85 |
| Critical continuous theory | p. 91 |
| Effective action | p. 91 |
| Correlation functions | p. 95 |
| Quadratic differences and Painleve equations | p. 98 |
| Notes | p. 104 |
| Spontaneous symmetry breaking, mean field | p. 107 |
| Mean field approximation | p. 108 |
| Dielectric constant of a polarizable medium | p. 108 |
| Classical spin model with a finite symmetry group | p. 112 |
| Continuous symmetry group | p. 118 |
| The Bethe approximation | p. 121 |
| Critical exponents | p. 125 |
| Lee-Yang zeroes | p. 131 |
| The Lee-Yang theorem | p. 132 |
| The one-dimensional case | p. 135 |
| General properties | p. 136 |
| Zeroes in the temperature plane | p. 139 |
| Large n limit | p. 140 |
| Saddle point method | p. 141 |
| Factorization | p. 145 |
| Coupling to an external field | p. 148 |
| Corrections to mean field | p. 151 |
| Laplace transform | p. 153 |
| Notes | p. 159 |
| Scaling transformations and the XY-model | p. 162 |
| Scaling laws. Real space renormalization | p. 162 |
| Homogeneity and scale invariance | p. 162 |
| Recurrence relations in real space | p. 168 |
| Examples and approximations | p. 176 |
| The XY-model | p. 193 |
| High temperature behaviour | p. 195 |
| Low temperature expansion. Vortices | p. 197 |
| The Villain action | p. 204 |
| Correlations | p. 207 |
| Renormalization flow | p. 213 |
| Two-dimensional systems with continuous symmetry | p. 219 |
| Magnetization inequality | p. 219 |
| Correlation inequality | p. 222 |
| Phenomenological renormalization | p. 224 |
| Notes | p. 230 |
| Continuous field theory and the renormalization group | p. 233 |
| The Lagrangian and dimensional analysis | p. 233 |
| Introduction | p. 233 |
| Generating functionals and dimensional analysis | p. 236 |
| The perturbative method | p. 242 |
| Diagrammatic series | p. 242 |
| Loop expansion | p. 246 |
| Evaluation of integrals and dimensional continuation | p. 250 |
| Group theoretical factors | p. 259 |
| Power counting | p. 261 |
| Perturbative renormalization | p. 264 |
| The renormalization group | p. 270 |
| Renormalization flow | p. 270 |
| Critical exponents | p. 280 |
| From the Gaussian ultraviolet fixed point to the infrared critical point in dimension less than four | p. 282 |
| Correlation functions at the critical point | p. 284 |
| Expansion near the critical point | p. 290 |
| Scaling laws below the critical temperature | p. 296 |
| Corrections to scaling laws | p. 301 |
| Deviation from the critical point in dimension lower than four | p. 301 |
| Logarithmic corrections in dimension four | p. 303 |
| Irrelevant operators | p. 307 |
| Numerical results | p. 310 |
| [varepsilon]-expansion of critical exponents | p. 311 |
| Equation of state | p. 313 |
| Amplitude ratios | p. 314 |
| Three-dimensional results | p. 317 |
| Multicritical points | p. 317 |
| Notes | p. 326 |
| Lattice gauge fields | p. 328 |
| Generalities | p. 328 |
| Presentation | p. 328 |
| The continuous limit | p. 332 |
| Order parameter and Elitzur's theorem | p. 341 |
| Duality | p. 345 |
| Structure of the phase diagram | p. 352 |
| Mean field approximation | p. 352 |
| Corrections to mean field and restoration of gauge invariance | p. 359 |
| Discrete groups: 1/d expansion | p. 362 |
| Continuous groups: computation of corrections | p. 365 |
| Strong coupling expansions | p. 371 |
| Convergence | p. 371 |
| Character expansions | p. 374 |
| Free energy | p. 380 |
| String tension and roughening transition | p. 385 |
| Mass spectrum | p. 390 |
| Lattice fermions | p. 393 |
| The doubling problem | p. 393 |
| The Nielsen-Ninomiya theorem | p. 396 |
| Staggered fermions | p. 399 |
| Notes | p. 401 |
| Index | |
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