Ising (conformal) fields and cluster area measures.

Camia, Federico; Newman, Charles M · Proc Natl Acad Sci U S A · 2009

basic_science · Level V

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Abstract

We provide a representation for the scaling limit of the d = 2 critical Ising magnetization field as a (conformal) random field by using Schramm-Loewner Evolution clusters and associated renormalized area measures. The renormalized areas are from the scaling limit of the critical 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.