1205.6610 (Federico Camia et al.)

Planar Ising magnetization field I. Uniqueness of the critical scaling
limit    [PDF]

Federico Camia, Christophe Garban, Charles M. Newman

The aim of this paper is to prove the following result. Consider the critical Ising model on the rescaled grid $a\Z^2$. Then, the renormalized magnetization field $$ \Phi^a:= a^{15/8} \sum_{x\in a\Z^2} \sigma_x \delta_x, $$ seen as a random distribution (i.e., generalized function) on the plane has a scaling limit as the mesh size $a\searrow 0$. The limiting field is conformally covariant and will be shown in \cite{\CGNproperties} to be non-Gaussian.

View original: http://arxiv.org/abs/1205.6610