This text is based on the experiment note for graduates and, as such, its style is basic education, requiring only some of the basics of mathematics, physics, statistics, and quantum field theory. However, it also contains some of the more complex concepts can be useful for researchers in this field. Each chapter will have a number of issues-guide the reader to a deeper understanding of some of the material presented in the main text-and, in many cases, there are also a number of lists of programs, short computer useful.
Table of Contents
1 Introduction 2 Path Integrals in Quantum and Statistical Mechanics 3 High-Dimensional Integrals 4 Monte Carlo Simulations in Quantum Mechanics 5 Scalar Fields at Zero and Finite Temperature 6 Classical Spin Models: An Introduction 7 Mean Field Approximation 8 Transfer Matrices, Correlation Inequalities and Roots of Partition Functions 9 High-Temperature and Low-Temperature Expansions 10 Peierls Argument and Duality Transformations 11 Renormalization Group on the Lattice 12 Functional Renormalization Group 13 Lattice Gauge Theories 14 Two-Dimensional Lattice Gauge Theories and Group Integrals 15 Fermions on a Lattice
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