Table of Contents

Introduction.- Path Integrals in Quantum and Statistical Mechanics.- High-Dimensional Integrals.- Monte-Carlo Simulations in Quantum Mechanics.- Scalar Fields at Zero and Finite Temperature.- Classical Spin Models: An Introduction.- Mean Field Approximation.- Transfer Matrices, Correlation Inequalities and Roots of Partition Functions.- High-Temperature and Low-Temperature Expansions.- Peierls Argument and Duality Transformations.- Renormalization Group on the Lattice.- Functional Renormalization Group.- Lattice Gauge Theories.- Two-dimensional Lattice Gauge Theories and Group Integrals.- Fermions on a Lattice.- Index.

Reviews

From the reviews:“This book fills a gap in the literature on non-pertubative aspects of field theories and numerical methods such as Monte Carlo which are usually covered only separately in different books. Providing a new perspective on statistical and quantum field theories, this book is useful for graduate students and researchers within and outside the field. … This book will definitely be a must-read for people who are active in the fields of statistical and quantum field theories.” (Mohammad R. Rahimi Tabar, Mathematical Reviews, October, 2013)“The book is well written, and pedagogically well-organized. The book has benefited by last-year undergraduate and beginning postgraduate students in physics and applied mathematics. … it also could be useful for researcher in the fields Note that each chapter ends with some problems which help to better understand the material given.” (Farruh Mukhamedov, zbMATH, Vol. 1268, 2013)