Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics (Hardcover)

。Comprehensive updated synthesis of statistical physics and quantum field theory
。Introduction to new and powerful methods of analysis
。Ideal combination of physical ideas and mathematical tools
。Self-contained introduction to many important areas of physics
。High-quality discussion and thorough analysis of many physical phenomena

This book provides a thorough introduction to the fascinating world of phase transitions as well as many related topics, including random walks, combinatorial problems, quantum field theory and S-matrix. Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry, and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides an excellent introduction to frontier topics of exactly solved models in statistical mechanics and quantum field theory, renormalization group, conformal models, quantum integrable systems, duality, elastic S-matrix, thermodynamics Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics, distinguished for their elegance and beauty, such as infinite dimensional algebras, conformal mappings, integral equations or modular functions.

Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail, paying attention to an overall coherent understanding of physical phenomena. Mathematical background is provided in supplements at the end of each chapter, when appropriate. The chapters are also followed by problems of different levels of difficulty. Advanced undergraduate and graduate students will find a rich and challenging source for improving their skills and for accomplishing a comprehensive learning of the many facets of the subject.

Table Of Contents

I: Introductory Notions

1: Introduction

2: One-dimensional systems

3: Approximate solutions

II: Bidimensional lattice models

4: Duality of two-dimensional Ising model

5: Combinatorial solutions of the Ising model

6: Transfer matrix of the two-dimensional Ising model

III: Quantum field theory and conformal variance

7: Quantum field theory

8: Renormalization group

9: Fermionic formulation of the Ising model

10: Conformal field theory

11: Minimal conformal models

12: Conformal field theory of free Bosonic and Fermionic fields

13: Conformal field theories with extended symmetries

14: The arena of conformal models

IV: Away from criticality

15: In the vicinity of the critical points

16: Integrable quantum field theories

17: S-matrix theory

18: Exact S-matrices

19: Thermodynamics Bethe Ansatz

20: Form factors and correlation functions

21: Non-integrable aspects