Monte Carlo Methods in Statistical Physics [Paperback]

M. E. J. Newman (Author), G. T. Barkema (Author)

Book Description

ISBN-10: 0198517971 | ISBN-13: 978-0198517979 | Publication Date: April 15, 1999

This book provides an introduction to Monte Carlo simulations in classical statistical physics and is aimed both at students beginning work in the field and at more experienced researchers who wish to learn more about Monte Carlo methods. It includes methods for both equilibrium and out of equilibrium systems, and discusses in detail such common algorithms as the Metropolis and heat-bath algorithms, as well as more sophisticated ones such as continuous time Monte Carlo, cluster algorithms, multigrid methods, entropic sampling and simulated tempering. Data analysis techniques are also explained starting with straightforward measurement and error-estimation techniques and progressing to topics such as the single and multiple histogram methods and finite size scaling. The last few chapters of the book are devoted to implementation issues, including lattice representations, efficient implementation of data structures, multispin coding, parallelization of Monte Carlo algorithms, and random number generation. The book also includes example programs which show how to apply these techniques to a variety of well-known models.

Editorial Reviews

Review

"This book is intended for those who are interested in the use of Monte Carlo simulations in classical statistical mechanics. Its primary goal is to explain how to perform such simulations efficiently. To this end, the authors discuss . . . some of the many interesting new algorithms designed to accelerate the simulation of particular classes of problems in statistical physics, such as cluster algorithms, multigrid methods, non-local algorithms for conserved-order-parameter models, entropic sampling, simulated tempering and continuous time Monte Carlo. The book is divided into three parts covering equilibrium (Chapters 1-8) and non-equilibrium (9-12) Monte Carlo simulations, and implementations (13-16). Each algorithm is introduced in the context of a particular model. For example, the Metropolis algorithm is illustrated by its application to the Ising model. A brief outline of the physics behind each model is always given."--Quarterly of Applied Mathematics

"In recent years there has been a flurry of activity in the development of new Monte Carlo algorithms that accelerate the dynamics of particular classes of systems in statistical physics. The present text discusses many of these algorithms . . . The book is well written and can be enjoyed at various levels. . . . [T]he primary goal of the book is to explain how to perform Monte Carlo simulations efficiently, and the authors have succeeded admirably in achieving their goal. The authors' discussion of the results of the algorithms was very helpful in understanding the algorithms. . . . In summary, this book belongs in the personal library of all researchers in statistical physics (regardless of whether they write Monte Carlo algorithms or not), computational scientists interested in Monte Carlo methods, and advanced undergraduates and graduate students wishing to learn about recent developments in statistical physics and Monte Carlo methods."--Journal of Statistical Physics

"Mark Newman and Gerard Barkema have written a remarkably clear and thorough book on the application of Monte Carlo simulations to classical statistical mechanics. Their writing is excellent throughout, and they cover a wide range of topics. Monte Carlo Methods in Statistical Physics is well suited for classroom use and could be valuable as a reference or tool for self-study for both beginning and experienced researchers. ... This book should give newcomers to Monte Carlo methods all the information and advice they need to get useful programs up and running. In addition to a basic presentation of the algorithms, Newman and Barkema discuss various implementation issues at length, give a wide range of programming advice, and discuss random number generators. This book also has an extensive treatment of data analysis techniques."--Computing in Science and Engineering

"The authors present a detailed account of Monte Carlo algorithms and techniques for the data analysis of the results of simulation. In my opinion this book can be very useful for both graduate students and experienced researchers. Problems are clearly stated, solutions are accurately discussed and there are problems to solve after every chapter. This book is surely suitable for use as a textbook for a course on simulation methods, or as a supplementary text in a course on statistical physics. Although the overall technical level is that of a graduate text, I think even experienced researchers in the field would benefit from reading the detailed accounts of the most sophisticated new simulation techniques which have appeared in recent years." -- Emilio N.M. Cirillo, Mathematical Reviews Clippings 2000m

About the Author

Mark Newman is at Santa Fe Institute. G. T. Barkema is at Utrecht University.

Product Details

• Paperback: 496 pages
• Publisher: Oxford University Press, USA (April 15, 1999)
• Language: English
• ISBN-10: 0198517971
• ISBN-13: 978-0198517979
• Product Dimensions: 9.2 x 6.2 x 1 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #836,555 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

11 of 11 people found the following review helpful:

5.0 out of 5 stars One of the best and up-to-date books in market, March 27, 2000

By 

Nilton (Florianopolis, Brazil) - See all my reviews

This review is from: Monte Carlo Methods in Statistical Physics (Paperback)

This book covers a wide range of applications in Statistical Mechanics, with clear explanation, examples, tips, algorithms, and explicit programs at the end of the book. It is good for beginners and experienced alike, since it discusses "classical" and modern algorithms. It is a must for those who want to make actual numerical calculations in Statistical Physics.

6 of 6 people found the following review helpful:

5.0 out of 5 stars The best Monte Carlo book ever, September 21, 2008

By 

Rohar - See all my reviews

Amazon Verified Purchase

This review is from: Monte Carlo Methods in Statistical Physics (Paperback)

This book is clearly written, well-organized and very user-friendly. I highly recommend this book to anyone interested in Monte Carlo methods.

Unlike many other books that focus on its applications, this book spends the first three chapters on a thorough explanation of the mechanism: how Monte Carlo methods work, Markov chain, detailed balance, ergodicity, and on how to measure their efficiency. The book is clear and thorough as it makes sense to an average physics student. However, it may not be so rigorous from a mathematician's viewpoint.

I particular like this book for its down-to-earth style. When the authors talk about an algorithm, they give their self-contained C/C++ code (beautifully written programs), and explain underlying principles, technical details as well as common pitfalls (e.g., random number generators), which are all very helpful.

The topics in this book are clearly physics-based, with a focus on Ising model and other related models. Many important topics are covered: cluster move, renormalization method, entropic sampling, tempering, etc.

However, I kind of feel that the lattice models may not deserve so much attention. One reason the authors choose to do so is perhaps that these models are so simple and so much fun. On the other hand, applications to molecular systems are not mentioned at all (well, most people prefer molecular dynamics instead of Monte Carlo for molecular systems anyway). So I should say that an average person interested in chemistry and biology may prefer some other books, e.g., Frenkel's book. But what you get from this book is a deep and enjoyable understanding, and you may not care about applications too much at the end. I should also mention that the book uses some nice (kind of like plastic) papers, which may feel a little weird at first.

1 of 2 people found the following review helpful:

4.0 out of 5 stars A practical book on Monte Carlo in Stat. Phy., July 11, 2006

By 

J. Ma "Big Bear" (CA, USA) - See all my reviews
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This review is from: Monte Carlo Methods in Statistical Physics (Paperback)

Overall, it's an excellent book on the practice of Monte Carlo and the c++ code in appendix are very instructive (Random Number Generators, Solid Monte Carlo Routines, etc.). It does have certain weaknesses though.

1) Sometimes the description are trivial in principle but written in great details. For example, on Pg 58 on the exact methods (so-called 'efficient way') of calculating averaged quantities from simulation.
2) Most of the content are heuristic. The discussion of the whole book is based on practice, although you do find something looks like a rigious proof (but no in fact). By rigious, I mean the proof should be based on Markov Chain and related properties of random process and statistical physics.

But as I said in the beginning, this is a invaluable book to anyone who wants to use Monte Carlo method in his/her domain. For myself, I am using this book as a reference to tackle functional optimization - Simulated Annealing, which is a very close sibling of Monte Carlo method.