%0 Journal Article
%T Planar Ising magnetization field I. Uniqueness of the critical scaling limit
%A Federico Camia
%A Christophe Garban
%A Charles M. Newman
%J Mathematics
%D 2012
%I arXiv
%R 10.1214/13-AOP881
%X The aim of this paper is to prove the following result. Consider the critical Ising model on the rescaled grid $a\mathbb{Z}^2$, then the renormalized magnetization field \[\Phi^a:=a^{15/8}\sum_{x\in a\mathbb{Z}^2}\sigma_x\delta_x,\] seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size $a\searrow0$. The limiting field is conformally covariant.
%U http://arxiv.org/abs/1205.6610v5