Criticalidade do modelo de Ising tridimensional : um estudo dinâmico

Abstract

In this work we investigate the criticality of the three-dimensional Ising model with interactions between rst neighbors. In our computational simulations we consider that the spins are distributed in a simple cubic lattice of side L, and lattice parameter a, so the number of spins in the lattice is N = (L=a)3. We employ periodical conditions of contour to describe the volumetric limit, in which the border and nite-size e ects are eliminated. We investigate the critical behavior of the system through the dynamic relaxation technique in short terms where the system evolves according to the Metropolis dynamic. Futhermore, the system properties are calculated before it reaches a state of equilibrium. Here, we consider only evolution from a completely ordered state, that is, the magnetization density of the system at the initial time is unitary. We calculate the magnetization (M), the structure factor (Sk), the time-dependent correlation length ( ), the uctuation of the order parameter (4m) and the second cumulante of Binder (U2). The value of the inverse of the critical temperature, Kc, was estimated using a method that explores the scale behavior of the derivative logarithm of the order parameter with respect to the logarithm of time (t; "), where " measures the distance to the critical point. The quantity (t; ") gives, besides the value of Kc, estimates for the critical exponents , and . The technique of data collapse is used for the purpose of obtaining greater accuracy in the values of the critical parameters obtained. The results found in this work for the critical parameter Kc = 0; 22166(3) and for the critical exponents = 0; 6495(3), = 1,2884(5) and = 0; 3222(3), were compared with others available in the recent specialized literature, for systems that are in the same class as the universality of the three-dimensional Ising model, in which we nd concordance until the fth decimal place through a technique that has a low computational requirement.