By Landau D.P., Binder K.
Facing all points of Monte Carlo simulation of advanced actual structures encountered in condensed-matter physics and statistical mechanics, this ebook offers an creation to desktop simulations in physics. This version now includes fabric describing strong new algorithms that experience seemed because the earlier variation was once released, and highlights contemporary technical advances and key functions that those algorithms now make attainable. Updates additionally contain a number of new sections and a bankruptcy at the use of Monte Carlo simulations of organic molecules. in the course of the ebook there are lots of purposes, examples, recipes, case experiences, and workouts to aid the reader comprehend the fabric. it really is excellent for graduate scholars and researchers, either in academia and undefined, who are looking to research innovations that experience develop into a 3rd software of actual technology, complementing test and analytical thought
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Additional resources for A Guide to Monte Carlo Simulations in Statistical Physics
Since physical processes, such as white noise generation from electrical circuits, generally introduce new numbers much too slowly to be effective with today’s digital computers, random number sequences are produced directly on the computer using software (Knuth, 1969). ) Since such algorithms are actually deterministic, the random number sequences which are thus produced are only ‘pseudo-random’ and do indeed have limitations which need to be understood. Thus, in the remainder of this book, when we refer to ‘random numbers’ it must be understood that we are really speaking of ‘pseudo-random’ numbers.
Most notable are two-dimensional XY-models with Hamiltonian X H ¼ ÀJ ðSix Sjx þ Siy Sjy Þ; ð2:26Þ nn where Si is a unit vector which may have either two components (plane rotator model) or three components (XY-model). These models develop no long range order at low temperature but have topological excitations, termed vortex–antivortex pairs, which unbind at the transition temperature TKT (Kosterlitz and Thouless, 1973). g. $ / expða"À# Þ; ð2:27Þ and every temperature below TKT is a critical point.
2 Special probability distributions and the central limit theorem Do we find any special behavior which arises when we consider a very large number of events? Consider two events A0 and A1 that are mutually exclusive and exhaustive: PðA1 Þ ¼ p; x ¼ 1; PðA0 Þ ¼ 1 À p; x ¼ 0: ð2:69Þ Suppose now that N independent samples of these events occur. Each outcome P is either 0 or 1, and we denote the sum X of these outcomes, X ¼ r¼1 xr . Now the probability that X ¼ n is the probability that n of the Xr were 1 and ðN À nÞ were 0.
A Guide to Monte Carlo Simulations in Statistical Physics by Landau D.P., Binder K.