Ising (conformal) fields and cluster area measures

F. Camia; C. M. Newman

doi:10.1073/pnas.0900700106

Ising (conformal) fields and cluster area measures

F. Camia, C. M. Newman

Mathematics

Research output: Contribution to Journal › Article › Academic › 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
Pages (from-to)	5547-5463
Number of pages	17
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
Publication status	Published - 2009

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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.",

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AU - Newman, C. 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.

U2 - 10.1073/pnas.0900700106

DO - 10.1073/pnas.0900700106

M3 - Article

SN - 0027-8424

VL - 106

SP - 5547

EP - 5463

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

IS - 14

ER -

Ising (conformal) fields and cluster area measures

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