Statistical Field Theory

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.