Métodos para simulação de SLE cordal

Abstract

Two dimensional models that simulate the phenomenon of phase transitions are common in statistical physics. It's believed that some models are conformally invariant in the system's critical region. If this assumption is true, in the continuum limit when the spacing of the mesh is zero, random traces that form the boundary of clusters at the phase transition could be described by a dynamic process called SLE. In this work we de ne chordal SLE, and talk about its connection to lattice models. We also show a method for numerical evaluation of the Loewner equation, using a method know as discret SLE; from which is possible to verify the convergence of lattice models which leads to a greater understanding of the behaviour of such systems, like getting their critical-point exponents. Finally, we shown an alternative form of the discrete SLE, producing a more eficient algorithm in most situations.