Monte Carlo Methods in Statistical Physics

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Clarendon Press, Feb 11, 1999 - Computers - 496 pages
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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. The material covered includes methods for both equilibrium and out of equilibrium systems, and common algorithms like the Metropolis and heat-bath algorithms are discussed in detail, 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 discussions of such topics as lattice representations, efficient implementation of data structures, multispin coding, parallelization of Monte Carlo algorithms, and random number generation. At the end of the book the authors give a number of example programmes demonstrating the applications of these techniques to a variety of well-known models.

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This book is an excellent text and has been an incredibly useful primer to the subject for me. The explanations are precise, mostly easy to follow and the material covered is vast, going from very simple Ising models to more complicated and often used systems like spin glasses, with important small details not being neglected. While there are some subject matters which feel missing, say.. more details on the Heisenberg models, what it does explain is sufficient to get you well on your way.
I would recommend this book as a great introduction to using Monte Carlo for studying classical spin systems as it has a nice overview of techniques used, such as Metropolis, cluster algorithms, some parallelism and it has some nice little code at the end to help jump into it and some exercises with solutions to help strengthen your understanding.

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About the author (1999)

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

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