PY 502, Computational Physics, Fall 2016 Monte Carlo simulations in classical statistical physics

Monte Carlo simulation is a very important class of stochastic methods for calculating thermal properties of many-particle systems—arguably these are the most important numerical techniques in statistical physics. Monte Carlo simulation methods are related to the elementary Monte Carlo integration methods that we discussed earlier, but are based on more efficient non-uniform sampling schemes. By using importance sampling, the configurations (particle positions, spin directions, etc.) of a finite but large many-body system (up to millions of degrees of freedom) can be generated according to the Bolzmann distribution, so that thermal expectation values are obtained as simple arithmetic averages of functions “measured” on the configurations.