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

Federico Camia, Christophe Garban, Charles M. Newman
2015 Annals of Probability  
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.
doi:10.1214/13-aop881 fatcat:c3ryk4ezvjc53axtwk5pyk3aie