Teorias conformes e evolução de Schramm-Loewner Estocástica

Abstract

The nature of a phase transition depends dramatically on the system s dimensionality and symmetries. In particular, the continuum phase transitions in two-dimensional systems possess an infinite dimensional symmetry group called the conformal group. Important quantities from the physical point of view, such as critical exponents and correlation functions, may be calculated using conformal symmetry. Recently, a new description of the geometrical properties of two-dimensional critical systems has been proposed without an underlying lattice realization, the so-called Stochastic Schramm-Loewner Evolution (SLE). This new formulation has attracted the attention of many physicists and mathematicians and has been awarded a Fields medal in 2006, given to W. Werner. The purpose of this dissertation is to present the fundamentals of conformal field theory from the algebraic point of view as well as from the SLE one. We illustrate these methods through their application in the most important model in statistical physics: the Ising model.