Monte Carlo investigations of phase transitions: status and perspectives

TL;DR

This paper reviews Monte Carlo methods using finite-size scaling to study critical phenomena, including Ising models and polymer systems, highlighting advances in cluster algorithms and scaling behavior above the marginal dimension.

Contribution

It provides an overview of recent Monte Carlo studies on phase transitions, emphasizing the application of cluster algorithms and finite-size scaling in complex models.

Findings

Cluster algorithms effectively describe crossover scaling functions.

Finite-size scaling applies to models above the marginal dimension.

Monte Carlo methods are valuable for studying critical phenomena.

Abstract

Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finite-size scaling in Ising models above the marginal dimension (d*=4) is discussed.