Ising (Conformal) Fields and Cluster Area Measures

Details Ising (Conformal) Fields and Cluster Area Measures Ising (Conformal) Fields and Cluster Area Measures

2008-12-21

arxiv.org/abs/0812.4030v1

Mathematics

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17 pages, 1 figure

Scientific paper

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.

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