Ising (Conformal) Fields and Cluster Area Measures
Probability
2022-06-08 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
We provide a representation for the scaling limit of the d=2 critical Ising magnetization field as a (conformal) random field using SLE (Schramm-Loewner Evolution) clusters and associated renormalized area measures. The renormalized areas are from the scaling limit of the critical FK (Fortuin-Kasteleyn) clusters and the random field is a convergent sum of the area measures with random signs. Extensions to off-critical scaling limits, to d=3 and to Potts models are also considered.
Keywords
Cite
@article{arxiv.0812.4030,
title = {Ising (Conformal) Fields and Cluster Area Measures},
author = {Federico Camia and Charles M. Newman},
journal= {arXiv preprint arXiv:0812.4030},
year = {2022}
}
Comments
17 pages, 1 figure