Download A Guide to Monte Carlo Simulations in Statistical Physics by Landau D.P., Binder K. PDF


By Landau D.P., Binder K.

Facing all facets of Monte Carlo simulation of advanced actual structures encountered in condensed-matter physics and statistical mechanics, this ebook presents an advent to machine simulations in physics. This version now comprises fabric describing strong new algorithms that experience seemed because the earlier variation used to be released, and highlights contemporary technical advances and key functions 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 publication there are various functions, examples, recipes, case experiences, and workouts to assist the reader comprehend the cloth. it really is perfect for graduate scholars and researchers, either in academia and undefined, who are looking to study recommendations that experience develop into a 3rd instrument of actual technological know-how, complementing test and analytical concept

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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. 2 Probability theory 35 One important topic which we shall not consider here is the question of the implementation of random number generators on massively parallel computers. In such cases one must be certain that the random number sequences on all processors are distinct and uncorrelated. As the number of processors available to single users increases, this question must surely be addressed, but we feel that at the present time this is a rather specialized topic and we shall not consider it further.

Predicting the phase diagram of simple atomic or molecular systems, as well as of mixtures, given the knowledge of the microscopic interactions, is an important task of statistical mechanics which relies on simulation methods quite strongly, as we shall see in later chapters. A much simpler phase diagram than for water occurs for the Ising ferromagnet with Hamiltonian X X 'i 'j À H 'i ; ð2:20Þ H ¼ ÀJnn nn i where 'i ¼ Æ1 represents a ‘spin’ at lattice site i which interacts with nearest neighbors on the lattice with interaction constant Jnn > 0.

7 makes a non-zero angle with the phase boundary, and a second scaling field t, which is tangential to the phase boundary at the tricritical point. In the vicinity of a multicritical point a ‘crossover’ scaling law is valid Fð"; H þ ; gÞ ¼ jgj2À" F ðH þ =jgjD" ; "=jgj0" Þ; ð2:42Þ where " is the specific heat exponent appropriate for a tricritical point, D" the corresponding ‘gap exponent’, and 0" a new ‘crossover’ exponent. In addition, there are power law relations which describe the vanishing of discontinuities as the tricritical point is approached from below.

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