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Applications of Monte Carlo methods to statistical physics

An introductory review of the Monte Carlo method for the statistical mechanics of condensed matter systems is given. Basic principles (random number generation, simple sampling versus importance sampling, Markov chains and master equations, etc) are explained and some classical applications (self-avoiding walks, percolation, the Ising model) are sketched. The finite-size scaling analysis of both second- and first-order phase transitions is described in detail, and also the study of surface and interfacial phenomena as well as the choice of appropriate boundary conditions is discussed. Only brief comments are given on topics such as applications to dynamic phenomena, quantum problems, and recent algorithmic developments (new sampling schemes based on reweighting techniques, nonlocal updating, parallelization, etc). The techniques described are exemplified with many illustrative applications.

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