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Full Description
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 a thorough introduction to the fascinating world of phase transitions and frontier topics of exactly solved models in statistical mechanics and quantum field theory, such as renormalization groups, conformal models, quantum integrable systems, duality, elastic S-matrices, thermodynamic 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, including infinite dimensional algebras, conformal mappings, integral equations and 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 while providing overall coherent understanding of physical phenomena. Mathematical background is made available in supplements at the end of each chapter, when appropriate. The chapters include problems of different levels of difficulty. Advanced undergraduate and graduate students will find this book a rich and challenging source for improving their skills and for attaining a comprehensive understanding of the many facets of the subject.
Contents
I. Preliminary Notions
1: Introduction
2: One-dimensional Systems
3: Approximate Solutions
II. Bidimensional Lattice Models
4: Duality of the 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 Invariance
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: Form Factors and Correlation Functions
V. Finite Size Effects
20: Thermodynamical Bethe Ansatz
21: Boundary Field Theory
VI Non-Integrable Aspects
22: Form Factor Perturbation Theory
23: Particle Spectrum by Semi-classical Methods
24: Interacting Fermions and Supersymmetric Models
25: Truncated Hilbert Space Approach
