Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models

A critical review is given of status and perspectives of Monte Carlo simula tions that address bulk and interfacial phase transitions of ferromagnetic Ising models. First, some basic methodological aspects of these simulations are briefly summarized (single-spin flip vs. cluster algorithms, finite-si ze scaling concepts), and then the application of these techniques to the n earest-neighbor Ising model in d = 3 and 5 dimensions is described. and a d etailed comparison to theoretical predictions is made. In addition, the cas e of Ising models with a large but finite range of interaction and the cros sover scaling from mean-field behavior to the Ising universality class are treated. If one considers instead a long-range interaction described by a p ower-law decay, new classes of critical behavior depending on the exponent of this power law become accessible, and a stringent test of the epsilon -e xpansion becomes possible. As a final type of crossover from mean-field typ e behavior to two-dimensional Ising behavior, the interface localization-de localization transition of Ising films confined between "competing'' walls is considered. This problem is still hampered by questions regarding the ap propriate coarse-grained model for the fluctuating interface near a wall, w hich is the starting paint for both this problem and the theory of critical wetting. :(C) 2001 Elsevier Science B,V. All rights reserved.