Monte Carlo Simulation in Statistical Physics : An Introduction

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. When Learning Very Formal Material One Comes To A Stage Where One Thinks One Has Understood The Material. Confronted With A Realiife Problem, The Passivity Of This Understanding Sometimes Becomes Painfully Elear. To Be Able To Solve The Problem, Ideas, Methods, Etc. Need To Be Ready At Hand. They Must Be Mastered (become Active Knowledge) In Order To Employ Them Successfully. Starting From This Idea, The Leitmotif, Or Aim, Of This Book Has Been To Elose This Gap As Much As Possible. How Can This Be Done? The Material Presented Here Was Born Out Of A Series Of Lectures At The Summer School Held At Figueira Da Foz (portugal) In 1987. The Series Of Lectures Was Split Into Two Concurrent Parts. In One Part The Formal Material Was Presented. Since The Background Of Those Attending Varied Widely, The Presentation Of The Formal Material Was Kept As Pedagogic As Possible. In The Formal Part The General Ideas Behind The Monte Carlo Method Were Developed. The Monte Carlo Method Has Now Found Widespread Appli­ Cation In Many Branches Of Science Such As Physics, Chemistry, And Biology. Because Of This, The Scope Of The Lectures Had To Be Narrowed Down. We Could Not Give A Complete Account And Restricted The Treatment To The Ap­ Plication Of The Monte Carlo Method To The Physics Of Phase Transitions. Here Particular Emphasis Is Placed On Finite-size Effects. 1. Introduction: Purpose And Scope Of This Volume, And Some General Comments -- 2. Theoretical Foundations Of The Monte Carlo Method And Its Applications In Statistical Physics -- 3. Guide To Practical Work With The Monte Carlo Method -- A1 Algorithm For The Random Walk Problem -- A2 Algorithm For Cluster Identification -- References. By Kurt Binder, Dieter W. Heermann. The Monte Carlo method is a computer simulation method which uses random numbers to simulate statistical fluctuations. The method is used to model complex systems with many degrees of freedom. Probability distributions for these systems are generated numerically and the method then yields numerically exact information on the models. Such simulations may be used tosee how well a model system approximates a real one or to see how valid the assumptions are in an analyical theory. A short and systematic theoretical introduction to the method forms the first part of this book. The second part is a practical guide with plenty of examples and exercises for the student. Problems treated by simple sampling (random and self-avoiding walks, percolation clusters, etc.) are included, along with such topics as finite-size effects and guidelines for the analysis of Monte Carlo simulations. The two parts together provide an excellent introduction to the theory and practice of Monte Carlo simulations Monte Carlo Simulation in Statistical Physics deals 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. Front Matter....Pages I-VIII Introduction: Purpose and Scope of this Volume, and Some General Comments....Pages 1-4 Theoretical Foundations of the Monte Carlo Method and Its Applications in Statistical Physics....Pages 5-67 Guide to Practical Work with the Monte Carlo Method....Pages 68-112 Back Matter....Pages 113-132