Monte Carlo Simulation in Statistical Physics: An Introduction

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The method is used to model complex systems with many degrees of freedom. Probability distributions for these systems are generated numerically and the method then yields numerically exact information on the models. Such simulations may be used to see how well a model system approximates a real one or to see how valid the assumptions are in an analytical theory.

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The difference is that this approach relies on equilibrium statistical mechanics rather than molecular dynamics. Instead of trying to reproduce the dynamics of a system, it generates states according to appropriate Boltzmann probabilities.

Thus, it is the application of the Metropolis Monte Carlo simulation to molecular systems. It is therefore also a particular subset of the more general Monte Carlo method in statistical physics.

classical and quantum monte carlo methods

It employs a Markov chain procedure in order to determine a new state for a system from a previous one. According to its stochastic nature, this new state is accepted at random. Each trial usually counts as a move.