Ising (conformal) fields and cluster area measures

Research output: Contribution to journalArticle

Abstract

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
Volume106
Issue number14
DOIs
StatePublished - Apr 7 2009

Keywords

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

ASJC Scopus subject areas

  • General

Cite this

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title = "Ising (conformal) fields and cluster area measures",
abstract = "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.",
keywords = "CLE, Continuum scaling limit, Critical Ising model, FK clusters, SLE",
author = "Federico Camia and Charles Newman",
year = "2009",
month = "4",
day = "7",
doi = "10.1073/pnas.0900700106",
language = "English (US)",
volume = "106",
pages = "5457--5463",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
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number = "14",

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AU - Camia, Federico

AU - Newman, Charles

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AB - 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.

KW - CLE

KW - Continuum scaling limit

KW - Critical Ising model

KW - FK clusters

KW - SLE

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JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

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