Abstract
Statistical mechanics of condensed matter systems in physics (fluids and solids) derives macroscopic equilibrium properties of these systems as averages computed from a Hamiltonian that describes the atomistic interactions in the system. While analytic methods for most problems involve uncontrolled approximations, Monte Carlo simulations allow numerically exact treatments, apart from statistical errors and from the systematic problem that finite systems are treated rather than the thermodynamic limit. However, this problem can be overcome by finite size scaling methods, and thus Monte Carlo methods have become a very powerful tool to study even complex phase transitions. Examples given will include unmixing of polymer blends, two-dimensional melting, etc.
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