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

Abstract

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 \[Φ^a:=a^{15/8}\sum_{x\in a\mathbb{Z}^2}σ_xδ_x,\] seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size $a\searrow 0$. The limiting field is conformally covariant.

Published in at http://dx.doi.org/10.1214/13-AOP881 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Two-Dimensional Critical Percolation: The Full Scaling Limit
• On the scaling limits of planar percolation
• Towards Conformal Invariance and a Geometric Representation of the 2D Ising Magnetization Field

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