Simulação de Monte Carlo: de modelos de spin à teoria de campos na rede - Pinheiro, M. P. de S [UNESP] (2007)
We review the application of the Monte Carlo method to a discrete spin model and to a scalar ﬁeld theory on the lattice with special emphasis on the Metropolis algorithm. Initially we consider an Ising spin model with long range interactions on a complex small world network. In view of the nonextensive nature of the model, we have have generalized the Metropolis algorithm to the Tsallis nonextensive thermostatistics. Numerical simulations with the generalized algorithm are implemented for two-and three-dimensional lattices. Next we review the lattice regularization method for the quantum theory of a selﬁnteracting scalar ﬁeld. We use the Metropolis algorithm to simulate the theory on the lattice and study the behavior of the renormalized quartic and sextic coupling constants as a function of the unrenormalized coupling constant. Results of simulations are presented for Euclidean lattices in two and three dimensions at intermediate and strong couplings