TABLE OF CONTENTS D.P.Landau
Center for Simulational Physics
The University of Georgia
Athens, Georgia 30602, U.S.A.
E-mail: dlandau@hal.physast.uga.edu
We provide an introduction to the use of Monte Carlo methods in statistical physics. The standard Metropolis algorithm is reviewed and then, in addition to providing a brief survey of a number of newer, accelerated techniques designed to avoid long time scales, we describe methods that are used to analyze data obtained for finite system size and finite run length. Lastly, we describe a novel, new approach, Wang-Landau sampling , that calculates the density of states of a system in an iterative method.
During the past half century there has been extensive study of phase transitions in an extremely broad range of models in statistical physics. From the theoretical perspective this has led to the development of relatively simple models that are readily soluble and seek to capture the essential qualitative features of real systems. To obtain the phase behavior of such models a wide variety of analytical techniques have been developed, but more recently, these approaches have been increasingly supplemented by computer simulations.
The fundamentals for the determination of phase behavior have long been understood statistical mechanics tells us that all the equilibrium thermodynamic properties can be determined once the partition function is known. However, the partition function is defined as a sum over all microstates of the system and is usually impossible to evaluate because the number of microstates is huge for all but the very smallest systems. As a consequence, exact...
