Monte Carlo Studies of Critical and Multicritical Phenomena

Abstract

In the late 1960s Monte Carlo studies of relatively simple lattice models began in earnest. Much of the work concentrated on contributing to our understanding of the effects of finite system size, finite sampling and metastabilities, boundary conditions, etc. In some cases these studies included complications in the system Hamiltonians although for the most part rather conventional systems were investigated. The first decade or so of this “serious” work was described in detail in [3.1]. Since then, there has been substantial growth in the use of Monte Carlo methods to study critical phenomena and a rapid expansion in the number of workers using this technique. Many recent studies involve rather complicated models and in many cases the ordered state was not even known prior to the simulation study. In addition, new methods such as Monte Carlo Renormalization Group (MCRG) techniques have been developed and used to augment, or even replace, standard Monte Carlo studies. (Since MCRG methods have been described in detail in [3.2], I need not describe them here. Another recently developed approach, the block distribution method, is described in Chap.1.) Results from Monte Carlo calculations are also used together with information obtained from other methods to understand various kinds of behavior. In this chapter recent studies of critical and multicritical phenomena primarily in models of adsorbed monolayers, surfaces, and bulk solids are reviewed.

Work supported in part by NSF grant No. DMR-8300754.