Monte Carlo method in statistical physics

Summary

In statistical physics, a Monte Carlo method estimates averages over the Boltzmann distribution of a system by sampling configurations at random. The configuration space is too large to sum over. So one runs a Markov chain whose stationary distribution is the Boltzmann distribution, as in the Metropolis–Hastings algorithm. Time averages along the chain then approximate thermal averages such as the energy or the magnetization. It is the main numerical tool for lattice models like the Ising model, for fluids, and for many quantum systems.