Monte Carlo investigations of phase transitions: status and perspectives

Using the concept of finite-size scaling, Monte Carlo calculations of vario us models have become a very useful tool for the study of critical phenomen a, with the system linear dimension as a variable. As an example, several r ecent studies of Ising models are discussed, as well as the extension to mo dels of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms. even the scaling functions describing the crossover fro m the Ising universality class to the mean-field behavior with increasing i nteraction range can be described. Additionally, the issue of finite-size s caling in Ising models above the marginal dimension (d* = 4) is discussed. (C) 2000 Elsevier Science B.V. All rights reserved.