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

Understand

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.