Thursday, May 31, 2012

1205.6610 (Federico Camia et al.)

Planar Ising magnetization field I. Uniqueness of the critical scaling

Federico Camia, Christophe Garban, Charles M. Newman
The aim of this paper is to prove the following result. Consider the critical Ising model on the rescaled grid $a\Z^2$. Then, the renormalized magnetization field $$ \Phi^a:= a^{15/8} \sum_{x\in a\Z^2} \sigma_x \delta_x, $$ seen as a random distribution (i.e., generalized function) on the plane has a scaling limit as the mesh size $a\searrow 0$. The limiting field is conformally covariant and will be shown in \cite{\CGNproperties} to be non-Gaussian.
View original:

No comments:

Post a Comment