Statistical Field Theory
An Introduction to Exactly Solved Models in Statistical Physics
Series: Oxford Graduate Texts;
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Product details:
- Publisher OUP Oxford
- Date of Publication 17 September 2026
- ISBN 9780197930366
- Binding Paperback
- No. of pages1024 pages
- Size 246x171 mm
- Language English 700
Categories
Short description:
This textbook provides a thorough introduction to phase transitions and exactly solved models in statistical physics and quantum field theory. It covers a broad area from basic concepts of statistical physics and quantum mechanics to latest developments in low dimensional quantum field theories, phase transitions and non-perturbative analysis.
MoreLong description:
This book is an introduction to Statistical Field Theory, an important subject of theoretical physics that has undergone formidable progress in recent years. It also 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, such as renormalization group, conformal models, boundary field theory, quantum integrable systems, duality, elastic S-matrix, thermodynamics Bethe ansatz, and form factor theory. It also addresses a powerful numerical technique, such as the Truncated Hilbert Space Approach, to extract non-perturbative quantities of quantum field theories, e.g. the mass spectrum, the scattering matrices, the presence of resonances, etc. Several chapters of the book are devoted to the semi-classical analysis of the spectrum of quantum field theories (both bosonic, fermionic or supersymmetric) and the breaking of integrability.
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.
Review from previous edition The book is well suited to provide access into this fascinating field of research and at the same time leads its readers all the way to the forefront of present research. It will provide a solid basis as a textbook for an advanced course in statistical physics, giving the lecturer an ample choice of topics supplemented by problem sets and references to the original literature.
Table of Contents:
I. Preliminary Notions
Introduction
One-dimensional Systems
Approximate Solutions
II. Bidimensional Lattice Models
Duality of the Two-dimensional Ising Model
Combinatorial Solutions of the Ising Model
Transfer Matrix of the Two-dimensional Ising Model
III. Quantum Field Theory and Conformal Invariance
Quantum Field Theory
Renormalization Group
Fermionic Formulation of the Ising Model
Conformal Field Theory
Minimal Conformal Models
Conformal Field Theory of Free Bosonic and Fermionic Fields
Conformal Field Theories with Extended Symmetries
The Arena of Conformal Models
IV. Away From Criticality
In the Vicinity of the Critical Points
Integrable Quantum Field Theories
S-Matrix Theory
Exact S Matrices
Form Factors and Correlation Functions
V. Finite Size Effects
Thermodynamical Bethe Ansatz
Boundary Field Theory
VI Non-Integrable Aspects
Form Factor Perturbation Theory
Particle Spectrum by Semi-classical Methods
Interacting Fermions and Supersymmetric Models
Truncated Hilbert Space Approach
