Towards Conformal Invariance and a Geometric Representation of the 2D Ising Magnetization Field

Abstract

We study the continuum scaling limit of the critical Ising magnetization in two dimensions. We prove the existence of subsequential limits, discuss connections with the scaling limit of critical FK clusters, and describe work in progress of the author with C. Garban and C.M. Newman.Comment: 20 pages, 1 figure, presented at the workshop "Inhomogeneous Random Systems" held at IHP (Paris) on January 26-27, 201