Estudo do modelo XY vetorial de Blume-Emery-Griffiths: aplicações a sistemas magnéticos e a filmes de misturas de 3He-4He - Joao Batista dos Santos Filho (2011)
The classical XY model, and an XY vectorial generalization of the Blume-Emery-Griffiths model (XY-VBEG), the latter one proposed by Berker and Nelson to describe the behavior of films of 3He-4He mixtures, are studied by Monte Carlo simulations. The models are treated intwo- and three-dimensions, where in the former lattice Berezinski-Kosterlitz-Thouless (BKT) transition is observed. We also study the XY-VBEG model on thin films structure and analyze its properties as a function of the film thickness. We employ extensive Monte Carlo simulations consisting of hybrid algorithms combining lattice-gas, Metropolis, Wolff and super-relaxation procedures in order to overcome the critical slowing down and correlations among different configurations of the systems. We also employed single histograms methods to get the corresponding transition temperatures. The XY model is treated on a cubic lattice with quenched dilution. The corresponding critical exponents are in the same universality class as the pure model, in agreement with the Harris criterion. Some good fittings with experimental results forthe critical temperature as a function of the dilution is obtained for two different crystals. On the other hand, thin films of the XY-VBEG model present a BKT transition, first-order transition as well tricritical, critical end, BKT end, and isolated critical points, depending on the valuesof the Hamiltonian parameters. The coalescence of the BKT end and the isolated critical points to a tricritical point, as a function of the film thickness, is also studied. Most of the XY-VBEG results are analyzed as an application to 3He-4He mixtures.