Ising (conformal) fields and cluster area measures

Federico Camia, Charles M. Newman

Research output: Contribution to journalArticlepeer-review


We provide a representation for the scaling limit of the d = 2 critical Ising magnetization field as a (conformal) randomfieldby 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.

Original languageEnglish (US)
Pages (from-to)5457-5463
Number of pages7
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number14
StatePublished - Apr 7 2009


  • CLE
  • Continuum scaling limit
  • Critical Ising model
  • FK clusters
  • SLE

ASJC Scopus subject areas

  • General

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