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March 2015 Planar Ising magnetization field I. Uniqueness of the critical scaling limit
Federico Camia, Christophe Garban, Charles M. Newman
Ann. Probab. 43(2): 528-571 (March 2015). DOI: 10.1214/13-AOP881

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

\[\Phi^{a}:=a^{15/8}\sum_{x\in a\mathbb{Z}^{2}}\sigma_{x}\delta_{x},\]

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.

Citation

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Federico Camia. Christophe Garban. Charles M. Newman. "Planar Ising magnetization field I. Uniqueness of the critical scaling limit." Ann. Probab. 43 (2) 528 - 571, March 2015. https://doi.org/10.1214/13-AOP881

Information

Published: March 2015
First available in Project Euclid: 2 February 2015

zbMATH: 1332.82012
MathSciNet: MR3305999
Digital Object Identifier: 10.1214/13-AOP881

Subjects:
Primary: 60G20, 60G60, 60K35, 82B20, 82B27

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 2 • March 2015
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