Monte Carlo method, classical fields and Bose statistics

In this paper we combine the classical fields method with the Monte Carlo approach for description of statistical properties of a Bose–Einstein condensate. We show that the canonical ensemble of interacting classical fields can be generated using Metropolis algorithm. We obtain a probability distribution of the condensate occupation for the weakly interacting Bose gas at low temperatures and pay a particular attention to the two momenta of this distribution: mean and variance of the condensate occupation.