By Kurt Binder, David P. Landau

ISBN-10: 0521842387

ISBN-13: 9780521842389

This new and up-to-date version bargains with all points of Monte Carlo simulation of advanced actual structures encountered in condensed-matter physics, statistical mechanics, and similar fields. After in brief recalling crucial heritage in statistical mechanics and chance concept, it provides a succinct assessment of easy sampling tools. The recommendations in the back of the simulation algorithms are defined comprehensively, as are the innovations for effective overview of method configurations generated by way of simulation. It comprises many purposes, examples, and routines to assist the reader and gives many new references to extra really expert literature. This variation encompasses a short evaluation of alternative tools of machine simulation and an outlook for using Monte Carlo simulations in disciplines past physics. this can be an exceptional advisor for graduate scholars and researchers who use desktop simulations of their learn. it may be used as a textbook for graduate classes on desktop simulations in physics and similar disciplines.

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**Sample text**

6 Phase diagram for the triangular Ising (lattice gas) model with antiferromagnetic nearest neighbor and ferromagnetic nextnearest neighbor interactions. T1 and T2 denote Kosterlitz– Thouless phase transitions and the + sign on the non-zero ﬁeld phase boundary is a tricritical point. The arrangement of open and closed circles shows examples of the two different kinds of ground states using lattice gas language. From Landau (1983). where i is the angle which a spin makes with the x-axis. Monte Carlo results (Landau, 1983), shown in Fig.

For a magnet the order parameter m, the speciﬁc heat C, the susceptibility 1 and the correlation length $ vary as (Stanley, 1971; Fisher, 1974) m ¼ mo " ; 1 ¼ 1o "À ; C ¼ Co "À ; $ ¼ $o "À# ; ð2:20aÞ ð2:20bÞ ð2:20cÞ ð2:20dÞ where " ¼ j1 À T=Tc j and the powers (Greek characters) are termed ‘critical exponents’. Note that Eqns. 20a–d) represent asymptotic expressions which are valid only as " ! 0 and more complete forms would include additional ‘corrections to scaling’ terms which describe the deviations from the asymptotic behavior.

The main utility of Monte Carlo methods is for problems which evade exact solution such as phase transitions, calculations of phase diagrams, etc. For this reason we shall emphasize this topic here. The study of phase transitions has long been a topic of great interest in a variety of related scientiﬁc disciplines and plays a central role in research in many ﬁelds of physics. Although very simple approaches, such as mean ﬁeld theory, provide a very simple, intuitive picture of phase transitions, they generally fail to provide a quantitative framework for explaining the wide variety of phenomena which occur under a range of different conditions and often do not really capture the conceptual features of the important processes which occur at a phase transition.

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

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