arXiv:0812.4030 Abstract | arXiv Analytics

arXiv:0812.4030 [math.PR]Abstract References Reviews Resources

Ising (Conformal) Fields and Cluster Area Measures

Published 2008-12-21Version 1

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.

Comments: 17 pages, 1 figure

Categories: math.PR, cond-mat.stat-mech, math-ph, math.MP

Subjects: 82B27, 60K35, 82B43, 60D05

Keywords: cluster area measures, scaling limit, random field, potts models, critical ising magnetization field

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