Catene di Markov Monte Carlo nei modelli di Ising

Abstract

This paper deals with an application of Monte Carlo Markov Chain. This Monte Carlo sampling technique was first introduced by Metropolis et al. to provide estimates of the statistical mechanical Boltzmann averages of parameters of a system of interacting particles. To illustrate an application of this method we have chosen the square spin-flip Ising model, i.e., a regular array of sites with each site occupied by a spin, which is allowed only two orientations. On such a model we have considered estimates of internal energy, magnetization, response functions and relaxation time, at the critical temperature and for different lattice sites. The problem of the accuracy of estimates is discussed in details and it has been shown how the moving block bootstrap can be applied successfully to assess standard errors and to construe confidence intervals for the computed averages. It can been seen also that, when correlation functions have a long-time behaviour, the moving block bootstrap works better than other methods based on subseries values.