by Daniel J Amit (Università di Roma, “La Sapienza”, Italy & Hebrew University, Israel) & Victor Martin-Mayor (Universidad Complutense de Madrid, Spain)

Table of Contents (190k)
Preface (130k)
Chapter 1: Pertinent Concepts and Ideas in the Theory of Critical Phenomena (259k)
Chapter 2: Formulation of the Problem of Phase Transitions in Terms of Functional Integrals (662k)
Chapter 3: Functional Integrals in Quantum Field Theory (510k)

This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. Non-perturbative methods and numerical simulations are introduced in this new edition. Abundant references to research literature complement this matter-of-fact approach. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.

The following new chapters are included:

I. Real Space Methods

II. Finite Size Scaling

III. Monte Carlo Methods. Numerical Field Theory

• Pertinent Concepts and Ideas in the Theory of Critical Phenomena
• Formulation of the Problem of Phase Transitions in Terms of Functional Integrals
• Functional Integrals in Quantum Field Theory
• Perturbation Theory and Feynman Graphs
• Vertex Functions and Symmetry Breaking
• Expansions in the Number of Loops and in the Number of Components
• Renormalization
• The Renormalization Group and Scaling the Critical Region
• The Computation of the Critical Exponents
• Beyond Leading Scaling
• Universality Revisited
• Critical Behavior with Several Couplings
• Crossover Phenomena
• Critical Phenomena near Two Dimensions
• Real Space Methods
• Finite Size Scaling
• Monte Carlo Methods. Numerical Field Theory