Abstract
For the statistical mechanics of many-body systems Monte Carlo methods have become a well-established tool. A particularly popular application is the study of statics and dynamics of phase transitions of lattice models. Here some aspects of these studies are reviewed, with a particular emphasis on problems illustrating general progress in the implementation of the method and in the analysis of the results. Finite-size effects will be given a detailed consideration, and finite-size scaling at both second- and first-order transitions will be discussed, as well as the study of inhomogeneous systems (containing interfaces or surfaces). Methods for sampling the entropy will be mentioned. Finally studies of diffusion problems and the simulation of the approach towards equilibrium in quenching experiments will be described. In the Conclusions those questions are pointed out where Monte Carlo methods still can give only rather unsatisfactory answers, such as equilibrium properties of strongly disordered systems.
Published Version
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