Monte Carlo Simulation in Statistical Physics

by Binder, Kurt; Heermann, Dieter W.

• ISBN13: 9783540432210
• ISBN10: 3540432213
• Edition: 4th
• Format: Hardcover
• Copyright: 2002-09-01
• Publisher: Springer Verlag

Summary

Monte Carlo Simulation in Statistical Physicsdeals with the computer simulation of many-body systems in condensed-matter physics and related fields of physics, chemistry and beyond, to traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, probability distributions are calculated, allowing the estimation of the thermodynamic properties of various systems. This book describes the theoretical background to several variants of these Monte Carlo methods and gives a systematic presentation from which newcomers can learn to perform such simulations and to analyze their results. This fourth edition has been updated and a new chapter on Monte Carlo simulation of quantum-mechanical problems has been added. To help students in their work a special web server has been installed to host programs and discussion groups (http://wwwcp.tphys.uni-heidelberg.de). Prof. Binder was the winner of the Berni J. Alder CECAM Award for Computational Physics 2001.

Table of Contents

Introduction: Purpose and Scope of this Volume, and Some General Comments	1	(4)
Theoretical Foundations of the Monte Carlo Method and Its Applications in Statistical Physics	5	(64)
Simple Sampling Versus Importance Sampling	5	(18)
Models	5	(1)
Simple Sampling	6	(2)
Random Walks and Self Avoiding Walks	8	(5)
Thermal Averages by the Simple Sampling Method	13	(1)
Advantages and Limitations of Simple Sampling	14	(3)
Importance Sampling	17	(3)
More About Models and Algorithms	20	(3)
Organization of Monte Carlo Programs, and the Dynamic Interpretation of Monte Carlo Sampling	23	(12)
First Comments on the Simulation of the Ising Model	23	(3)
Boundary Conditions	26	(3)
The Dynamic Interpretation of the Importance Sampling Monte Carlo Method	29	(4)
Statistical Errors and Time-Displaced Relaxation Functions	33	(2)
Finite-Size Effects	35	(33)
Finite-Size Effects at the Percolation Transition	35	(4)
Finite-Size Scaling for the Percolation Problem	39	(3)
Broken Symmetry and Finite-Size Effects at Thermal Phase Transitions	42	(2)
The Order Parameter Probability Distribution and Its Use to Justify Finite-Size Scaling and Phenomenological Renormalization	44	(10)
Finite-Size Behavior of Relaxation Times	54	(3)
Finite-Size Scaling Without ``Hyperscaling''	57	(1)
Finite-Size Scaling for First-Order Phase Transitions	58	(7)
Finite-Size Behavior of Statistical Errors and the Problem of Self-Averaging	65	(3)
Remarks on the Scope of the Theory Chapter	68	(1)
Guide to Practical Work with the Monte Carlo Method	69	(46)
Aims of the Guide	72	(2)
Simple Sampling	74	(21)
Random Walk	74	(8)
Nonreversal Random Walk	82	(1)
Self Avoiding Random Walk	83	(4)
Percolation	87	(8)
Biased Sampling	95	(3)
Self-Avoiding Random Walk	95	(3)
Importance Sampling	98	(17)
Ising Model	98	(14)
Self-Avoiding Random Walk	112	(3)
Some Important Recent Developments of the Monte Carlo Methodology	115	(22)
Introduction	115	(2)
Application of the Swendsen--Wang Cluster Algorithm to the Ising Model	117	(5)
Reweighting Methods in the Study of Phase Diagrams, First-Order Phase Transitions, and Interfacial Tensions	122	(5)
Some Comments on Advances with Finite-Size Scaling Analyses	127	(10)
Quantum Monte Carlo Simulations: An Introduction	137	(22)
Quantum Statistical Mechanics vs. Classical Statistical Mechanics	137	(6)
The Path Integral Quantum Monte Carlo Method (PIMC)	143	(7)
Quantum Monte Carlo for Lattice Models	150	(8)
Concluding Remarks	158	(1)
Appendix	159	(6)
A.1 Algorithm for the Random Walk Problem	159	(1)
A.2 Algorithm for Cluster Identification	160	(5)
References	165	(10)
Bibliography	175	(2)
Subject Index	177