Trasição de fase topológica no modelo de Heisenberg anisotrópico em duas dimensões

Abstract

The importance of topological excitations in physics, mainly in the description of phase transitions, has a long history beginning with the superconductivity phenomenon in the rst years of the last century. However, the ideas behind this new concept has been more accurately described by Kosterlitz and Thouless, about 40 years ago. Conductor-superconductor, uidsuperuid, rough transitions and many others are characterized as being due the appearance of topological excitations in the system. Another concept of great importance is that the universality in phase transitions . Close to a phase transition the correlations of the system become innity, so that, the details of the model become irrelevant. In this situation, systems originaly so dierent as superconductors and ferromagnets, can be described by the same theory. The critical expoents, that caracterize the transition, depend only on the system dimension, the range of the potential and of their symmetries. This work is dedicated to study of the anisotropic Heisenberg model in two dimensions. This model has a non-usual phase transition, with quasi-long range order, characterized by a change in the behavior of the spin-spin correlation function C(r). In low temperature, T < TBKT, C(r) decays as a power law with distance, r. For temperatures greater than TBKT the correlation function falls o exponencially. The free energy has all the continuous derivatives, for this reason the transition is known as innity order transition. The BKT teory assume that the transition is driven by a vortice-antivortice unbiding mechanism in the system. In our study we did extensive numerical simulations with the tecnique known as Replica Exchange Wang-Landau. This method allow us to estimate the density of states g(E) of the model. With g(E) we can calculated the relevant termodynamic functions of the system (energy, magnetization, suceptibility and correlations for instance). Using Finite Size Scaling tecniques we have determinade the transition temperature TBKT and the behavior of the correlation function for a large range of temperatures. The calculations were done for various dilutions of non-magnetic sites, p, with p = 0,0;0,20;0,30 e 0,35, that allowed us to describe with great precision the critical behavior of the model in particular the correlation lentgh