Statistical Field Theory An Introduction to Exactly Solved Models in Statistical Physics

A thorough and pedagogical introduction to phase transitions and exactly solved models in statistical physics and quantum field theory.

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.

1 - Introduction
2 - One-dimensional systems
3 - Approximate solutions
4 - Duality of two-dimensional Ising model
5 - Combinatorial solutions of the Ising model
6 - Transfer matrix of the two-dimensional Ising model
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
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

Giuseppe Mussardo has been Professor of Theoretical Physics at the International School for Advanced Studies (ISAS) in Trieste since 2000, and was Deputy Director of ISAS 2001-2004. He is Head of the Statistical Physics group at ISAS and Coodinator of the European Science Foundation grant INSTANS. He edits Nuclear Physics B: Statistical Mechanics and Field Theory, and JSTAT.