Ising (conformal) fields and cluster area measures

Federico Camia; Charles M. Newman

doi:10.1073/pnas.0900700106

Ising (conformal) fields and cluster area measures

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	5457-5463
Number of pages	7
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	106
Issue number	14
DOIs	https://doi.org/10.1073/pnas.0900700106
State	Published - Apr 7 2009

Keywords

CLE
Continuum scaling limit
Critical Ising model
FK clusters
SLE

ASJC Scopus subject areas

General

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10.1073/pnas.0900700106

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AU - Newman, Charles M.

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

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ER -

Ising (conformal) fields and cluster area measures

Abstract

Keywords

ASJC Scopus subject areas

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