Introdução ao método Monte Carlo: exemplos de aplicação

Abstract

In the present work, we study the Monte Carlo method in an introductory level. This method has been applied in models and systems whose results are known to compare with ours results. In the first part of this work, some concepts of probability and statistics related with the Monte Carlo method are study. By using these concepts the Metropolis’ algorithm is presented. The main objective of this algorithm is calculate averages of physics properties which are obtained by ensembles of configurations generated from random walks in the configurational space. We apply the Metropolis’ algorithm in the Ising model to study ferromagnetism of localized moments in a bidimensional system. The behavior of the spontaneous magnetization is observed when the temperature is changed in the absence of external magnetic field. We have been also analysed the behavior of the magnetization in an external magnetic field for some values of temperature. In the last part of this work, we have been studied the Variational Monte Carlo method. This method is based in the variational principle of quantum mechanics. It calculates the mean value of the energy by applying the variational principle. In this work the Variational Monte Carlo method has been applied, together with the Metropolis’ algorithm, to calculate the energy of the ground state for a particle in an infinite square well.