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arXiv · 0812.4030

Ising (Conformal) Fields and Cluster Area Measures

Federico Camia·Charles M. Newman
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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 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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BibTeXRIS

Federico Camia, Charles M. Newman. 2008-12-21. Ising (Conformal) Fields and Cluster Area Measures. https://doi.org/10.1073/pnas.0900700106

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