Monte-Carlo methods

Numerical techniques for computing integrals by using pseudo-random numbers are generically referred to as Monte Carlo methods. After an elementary introduction of the basic concepts, explanations are given on how these techniques apply to the computation of statistical mechanical integrals, that is to say of thermodynamic quantities in various statistical mechanical ensembles. The implementation of atomistic Monte Carlo is considered with emphasis on pseudo-random number generators. Finally, we present the principles of few extended Monte Carlo techniques together with few examples taken from the literature.