Some ten years ago, when completing with J.-B. Zuber a previous text on Quantum Field Theory, the senior author was painfully aware that little mention was made that methods in statistical physics and Euclidean field theory were coming closer and closer, with common tools based on the use of path integrals and the renormalization group giving insights on global structures. It was partly to fill this gap that the present book was undertaken. Alas, over the five years that it took to come to life, both subjects have undergone a new evolution. Disordered media, growth patterns, complex dynamical systems or spin glasses are among the new important topics in statistical mechanics, while superstring theory has turned to the study of extended systems, Kaluza-Klein theories in higher dimensions, anticommuting coordinates……

Contents of Volume 1

Preface

7 Diagrammatic methods

7.1 General Techniques

7.2 Series expansions

7.4 Results and analysis

Notes

8 Numerical simulations

8.1 Algorithms

8.2 Extraction of results in a simulation

Notes

9 Conformal invariance

9.1 Energy-momentum tensor - Virasoro algebra

9.2 Examples

9.3 Finite size effects and modular invariance

9.A Jacobian 6-series and products

9.B Superconformal algebra

9.C Current algebra

Notes

10 Disordered systems and fermionic methods

10.1 One-dimensional models

10.2 Two-dimensional electron gas in a strong field

10.3 Random matrices

10.4 The planar approximation

10.5 Spin systems with random interactions

Notes

11 Random geometry

11.1 Random lattices

11.2 Random surfaces

Notes

Index