Download PDF by Kurt Binder, David P. Landau: A Guide to Monte Carlo Simulations in Statistical Physics

By Kurt Binder, David P. Landau

ISBN-10: 0521768489

ISBN-13: 9780521768481

Facing all facets of Monte Carlo simulation of advanced actual structures encountered in condensed-matter physics and statistical mechanics, this ebook presents an creation to laptop simulations in physics. This variation now includes fabric describing strong new algorithms that experience seemed because the past version used to be released, and highlights contemporary technical advances and key purposes that those algorithms now make attainable. Updates additionally comprise a number of new sections and a bankruptcy at the use of Monte Carlo simulations of organic molecules. in the course of the booklet there are numerous functions, examples, recipes, case experiences, and routines to assist the reader comprehend the fabric. it's perfect for graduate scholars and researchers, either in academia and undefined, who are looking to study suggestions that experience develop into a 3rd device of actual technological know-how, complementing test and analytical conception.

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Extra info for A Guide to Monte Carlo Simulations in Statistical Physics

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Then one can ask whether these quantities are correlated, or whether the fluctuations of these quantities are independent of each other. Consider the NVT ensemble where entropy S and the pressure p (an intensive variable) are the (fluctuating) conjugate variables fp ¼ Àð@F=@V ÞNT , S ¼ Àð@F=@TÞNV g. What are the fluctuations of S and p, and are they correlated? The answer to these questions is given by   ðÁSÞ2 NVT ¼ kB Cp ; ð2:17aÞ  2 ðÁpÞ NVT ¼ ÀkB Tð@p=@V ÞS ; ð2:17bÞ   ð2:17cÞ ðÁSÞðÁpÞ NVT ¼ 0: One can also see here an illustration of the general principle that fluctuations of extensive variables (like S) scale with the volume, while fluctuations of intensive variables (like p) scale with the inverse volume.

The practitioner is now faced anew with the challenge of testing the random number generator for each high resolution application, and we shall review some of the ‘tests’ later in this section. The generators which are discussed in the next sub-sections produce a sequence of random integers. Usually floating point numbers between 0 and 1 are needed; these are obtained by carrying out a floating point divide by the largest integer Nmax which can fit into a word. One important topic which we shall not consider here is the question of the implementation of random number generators on massively parallel computers.

In fact, these two choices will give the same stream of numbers but in reverse order; the quality of each sequence is thus the same. In general, higher quality of random number sequences results when large values of p and q are used although for many purposes R250 works quite well. In order for the quality of the random number sequence to be of the highest possible quality, it is important for the ‘table’ to be properly initialized. One simple method is to use a good congruential generator to generate the initial values; the best procedure is to use a different random number to determine each bit in succession for each entry in the initial table.

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A Guide to Monte Carlo Simulations in Statistical Physics by Kurt Binder, David P. Landau

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