How Monte Carlo simulations can clarify complex problems in statistical physics

Statistical mechanics of condensed matter systems in physics (fluids and so lids) derives macroscopic equilibrium properties of these systems as averag es 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 prob lem can be overcome by finite size scaling methods, and thus Monte Carlo me thods have become a very powerful tool to study even complex phase transiti ons. Examples given will include unmixing of polymer blends, two-dimensiona l melting, etc.