Monte Carlo investigations of phase transitions: status and perspectives

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

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23 pages, including 14 PostScript figures. Presented at StatPhys-Taiwan, August 9-16, 1999. Also available as PDF file at ht

Scientific paper

10.1016/S0378-4371(00)00025-X

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.

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