Search results for "Monte Carlo method in statistical physics"

CLUSTER MONTE CARLO ALGORITHMS IN STATISTICAL MECHANICS

1992

The cluster Monte Carlo method, where variables are updated in groups, is very efficient at second order phase transitions. Much better results can be obtained with less computer time. This article reviews the method of Swendsen and Wang and some of its applications.

Group Metropolis Sampling

2017

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. Two well-known class of MC methods are the Importance Sampling (IS) techniques and the Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce the Group Importance Sampling (GIS) framework where different sets of weighted samples are properly summarized with one summary particle and one summary weight. GIS facilitates the design of novel efficient MC techniques. For instance, we present the Group Metropolis Sampling (GMS) algorithm which produces a Markov chain of sets of weighted samples. GMS in general outperforms other multiple try schemes…

Theoretical Foundations of the Monte Carlo Method and Its Applications in Statistical Physics

2002

In this chapter we first introduce the basic concepts of Monte Carlo sampling, give some details on how Monte Carlo programs need to be organized, and then proceed to the interpretation and analysis of Monte Carlo results.

Monte Carlo Simulations of Alloy Phase Transformations

1994

The use of Monte Carlo simulation methods for study of order-disorder phase transitions in lattice models of alloys is reviewed, with an emphasis on interfacial phenomena and the kinetics of ordering and/or phase separation. Topics discussed include the attempt to predict the phase diagram of Fe-Al alloys from recent measurements of effective interaction parameters, competition between magnetic and crystallographic ordering in such alloys, and the structure of their antiphase domain boundaries. Both an interfacial roughening transition of this domain wall and interfacial enrichment phenomena are predicted. Then simulations of alloy-vacuum surfaces are discussed, and it is shown that both ca…

Monte Carlo Simulations of Polymer Systems

1988

The impact of Monte Carlo “computer experiments” in polymer physics is described, emphasizing three examples taken from the author’s research group. The first example is a test of the classical Flory—Huggins theory for polymer mixtures, including a discussion of cricital phenomena. Also “technical aspects” of such simulations (“grand-canonical” ensemble, finite—size scaling, etc.) are explained briefly. The second example refers to configurational statistics and dynamics of chains confined to cylindrical tubes; the third example deals with the adsorption of polymers at walls. These simulations check scaling concepts developed along the lines of de Gennes.

Monte Carlo Simulations in Polymer Science

2012

Monte Carlo methods are useful for computing the statistical properties of both single macromolecules of various chemical architectures and systems containing many polymers (solutions, melts, blends, etc.). Starting with simple models (lattice models such as the self-avoiding walk or the bond fluctuation model, as well as coarse-grained or chemically realistic models in the continuum) various algorithms exist to generate conformations typical for thermal equilibrium, but dynamic Monte Carlo methods can also model diffusion and relaxation processes (as described by the Rouse and the reptation models for polymer melt dynamics). Limitations of the method are explained, and also the measures to…

Monte Carlo Methods for the Sampling of Free Energy Landscapes

2019

In this chapter, we return to classical statistical mechanics, wherein the canonical ensemble averages of an observable \(A(\overrightarrow{x})\), where \(\overrightarrow{x} \) stands symbolically for the “microstate” coordinate in the configurational part of the phase space of the system, are given by (cf. Sect. 2.1.1)

Monte carlo methods in quantum many-body theories

2008

This is an introduction of Monte Carlo methods for beginners and their application to some quantum many-body problems. Special emphasis is done on the methodology and the general characteristics of Monte Carlo calculations. An introduction to the applications to many-body physics, specifically the Variational Monte Carlo and the Green Function Monte Carlo, is also included.

Off-lattice models

2005

A Monte Carlo Simulation of the Stillinger-Weber Model for Si-Ge Alloys

1994

ABSTRACTThe bulk phase behavior of silicon-germanium alloys is investigated by means of a constant pressure Monte Carlo simulation of the Stillinger-Weber potential in the semi-grand-canonical ensemble. At low temperatures, Si and Ge phase separate into a Si-rich phase and a Ge-rich phase. The two-phase region is terminated by a critical point whose nature is investigated thoroughly by the multihistogram method combined with finite size scaling analysis. These results showed that the critical behavior of the alloy belongs to the mean field universality class, presumably due to the elastic degrees of freedom. We have also studied the structural properties of the mixture and found that the li…