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

Authors
Camia, Federico Garban, Christophe Newman, Charles M.
Citation
Camia, Federico et al., Planar Ising magnetization field I. Uniqueness of the critical scaling limit, Annals of probability , 43(2), 2015, pp. 528-571
Journal title
Annals of probability → ACNP
ISSN journal
00911798
Volume
43
Issue
2
Year of publication
2015
Pages
528 - 571
Database
ACNP
SICI code
Abstract
The aim of this paper is to prove the following result. Consider the critical Ising model on the rescaled grid aZ2 , then the renormalized magnetization field .a:=a15/8.x.aZ2.x.x, seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size a.0 . The limiting field is conformally covariant.