发现论坛里似乎没有，就传上来了。不知道应该发到哪个板块，先暂时发这儿了，以下是preface

The material presented in this book was born out of a series of lectures at a
Summer School held at Figueira da Foz (Portugal) in 1987. Since then, the field
of computational physics has seen an enormous growth and stormy development.
Many new applications and application areas have been found. In the 1980s, we
could not foresee this but hoped that theMonte Carlo method would find such widespread
acceptance. We were thus very glad to bring the work forward to a second
edition correcting some misprints. Since then and over the years and editions of this
book, many chapters have been added accounting for the development of new methods
and algorithms. However, the basics have remained stable over the years and
still serve as an entry point for researchers who would like to apply the Monte Carlo
method and perhaps want to develop new ideas. Appending these basics with chapters
on newly developed methods has evolved this book a bit into the direction of
a textbook giving an introduction and at the same time covering a very broad spectrum.
The first part of the book explains the theoretical foundations of the Monte
Carlo method as applied to statistical physics. Chapter 3 guides the reader to practical
work by formulating simple exercises and giving hints to solve them. Hence,
it is a kind of “primer” for the beginner, who can learn the technique by working
through these two chapters in a few weeks of intense study. Alternatively, this
material can be used as text for a short course in university teaching covering in
one term. The following chapters describe some more sophisticated and advanced
techniques, e.g., Chap. 4 describes cluster algorithms and reweighting techniques,
Chap. 5 describes the basic aspects of quantum Monte Carlo methods, and Chap. 6
(newly added to the 5th edition) describes recent developments in the last decade,
such as “expanded ensemble” methods to sample the energy density of states, e.g.,
the Wang–Landau algorithm, as well as methods to sample rare events, such as
“transition path sampling”. These chapters then should be useful even for the more
experienced practitioner. However, no attempt is made to cover all existing applications
of Monte Carlo methods to statistical physics in an encyclopedic style –
such an attempt would make this book almost unreadable and unhandy. While the
“classic” applications of Monte Carlo methods in the 1970s and 1980s of the last
century now are simple examples that a student can work out on his laptop as an
exercise, this is not true for the recent developments described in the last chapter,
of course, which often need heavy investment of computer time. Hence, no attempt
could as yet be made to enrich the last chapters with exercises as well.
We are very grateful for the many comments, suggestions, and the pointing out
of misprints that have been brought to our attention. We would like to thank the
many colleagues with whom we had the pleasure to engage with into discussions
and that in some way or the other have shaped our thinking and thus have indirectly
influenced this work.
Mainz, Heidelberg Kurt Binder
July 2010 Dieter W. Heermann


以下是目录

1 Introduction: Purpose and Scope of This Volume, and Some
General Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Theoretical Foundations of the Monte Carlo Method
and Its Applications in Statistical Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Simple Sampling Versus Importance Sampling.. . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Simple Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.3 RandomWalks and Self-AvoidingWalks . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.4 Thermal Averages by the Simple Sampling Method . . . . . . . . . . . 13
2.1.5 Advantages and Limitations of Simple Sampling . . . . . . . . . . . . . . 14
2.1.6 Importance Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.7 More About Models and Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Organization ofMonte Carlo Programs, and the Dynamic
Interpretation ofMonte Carlo Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 First Comments on the Simulation of the Ising Model . . . . . . . . . 23
2.2.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.3 The Dynamic Interpretation of the Importance
SamplingMonte CarloMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.4 Statistical Errors and Time-Displaced Relaxation Functions . . 32
2.3 Finite-Size Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.1 Finite-Size Effects at the Percolation Transition.. . . . . . . . . . . . . . . 35
2.3.2 Finite-Size Scaling for the Percolation Problem.. . . . . . . . . . . . . . . 38
2.3.3 Broken Symmetry and Finite-Size Effects
at Thermal Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.3.4 The Order Parameter Probability Distribution
and Its Use to Justify Finite-Size Scaling
and PhenomenologicalRenormalization.. . . . . . . . . . . . . . . . . . . . . . . 44
2.3.5 Finite-Size Behavior of Relaxation Times . . . . . . . . . . . . . . . . . . . . . . 52
2.3.6 Finite-Size Scaling Without “Hyperscaling” . . . . . . . . . . . . . . . . . . . 56
2.3.7 Finite-Size Scaling for First-Order Phase Transitions . . . . . . . . . . 56
2.3.8 Finite-Size Behavior of Statistical Errors
and the Problem of Self-Averaging.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.4 Remarks on the Scope of the Theory Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3 Guide to PracticalWork with the Monte Carlo Method . . . . . . . . . . . . . . . . . . 69
3.1 Aims of the Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.2 Simple Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.1 RandomWalk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.2 Nonreversal RandomWalk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.2.3 Self-Avoiding RandomWalk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.2.4 Percolation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.3 Biased Sampling .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.3.1 Self-Avoiding RandomWalk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4 Importance Sampling.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.4.1 Ising Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.4.2 Self-Avoiding RandomWalk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110
4 Some Important Recent Developments of the Monte Carlo
Methodology .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111
4.1 Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111
4.2 Application of the Swendsen–Wang Cluster Algorithm
to the IsingModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113
4.3 Reweighting Methods in the Study of Phase Diagrams,
First-Order Phase Transitions, and Interfacial Tensions . . . . . . . . . . . . . . . .118
4.4 Some Comments on Advances with Finite-Size Scaling Analyses . . . .123
5 Quantum Monte Carlo Simulations: An Introduction. . . . . . . . . . . . . . . . . . . . .131
5.1 Quantum Statistical Mechanics Versus Classical
Statistical Mechanics .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131
5.2 The Path Integral QuantumMonte Carlo Method . . . . . . . . . . . . . . . . . . . . . .137
5.3 Quantum Monte Carlo for Lattice Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143
5.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .152
6 Monte Carlo Methods for the Sampling of Free Energy Landscapes . . . .153
6.1 Introduction and Overview.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153
6.2 Umbrella Sampling .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .161
6.3 Multicanonical Sampling and Other “Extended
Ensemble” Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164
6.4 Wang–Landau Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166
6.5 Transition Path Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169
6.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .173
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175
A.1 Algorithm for the RandomWalk Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175
A.2 Algorithm for Cluster Identification .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .193
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .197