Estudo computacional estático e dinâmico do modelo clássico de Heisenberg ferromagnético isotrópico

Abstract

We studied the energy, the magnetization and cumulants of the three-dimesional isotropic Heisenberg model in the phase transition region by using Metropolis algorithm. In order to study the critical temperature we implemented the vectorized Metropolis, hybrid Metropolis and Wolff (the latter one as prescribed by Chen et al (4)). We choseMetropolis:Overrelaxation 1:4 for its fastest independent measurements yield. We implemented Bereau and Swendsen's optimized multi- histogram technique (13) for this study. We obtained through finite size scaling the critical exponents = -0, 0709 +- 0,0099, = 0,3499 +- 0,0076, = 1,3880 +- 0,0060 and = 0,6903 +- 0,0034, the inverse criticaltemperature Kc = 0; 69314 +- 0,00032, and the universal parameter Binder cumulant for an infinite lattice at critical temperature U4B = 0, 62178 +- 0,00049 by means of a strategy involving jackknife to reduce bias. These exponents agree with experimental, theoretical and simulational determinations from literature. We also investigated energy and spin time autocorrelations in unidimensional lattices (an integrable L = 4 system and a non-integrable L = 18 system), by integration with fourth order Runge-Kutta, Predictor-Corrector, Suzuki-Trotter and optimized Forest-Ruth methods. We found that the use of quad precision, an integration step of approximately 10..6, N = 106 sampling, and longspin chains may be sucient to discriminate between an expected and an anomalous spin diffusion. Besides, each algorithm implementation may correspond to a dierent time operator for the non-integrable system.