Planar ising magnetization field I. uniqueness of the critical scaling limit

Federico Camia; Christophe Garban; Charles M. Newman

doi:10.1214/13-AOP881

Planar ising magnetization field I. uniqueness of the critical scaling limit

Federico Camia, Christophe Garban, Charles M. Newman

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

Abstract

The aim of this paper is to prove the following result. Consider the critical Ising model on the rescaled grid aZ², then the renormalized magnetization field Φ^a := a^15/8 ∑ _x∈aZ² σ_xδ_x, seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size a ↓ 0. The limiting field is conformally covariant.

Original language	English (US)
Pages (from-to)	528-571
Number of pages	44
Journal	Annals of Probability
Volume	43
Issue number	2
DOIs	https://doi.org/10.1214/13-AOP881
State	Published - 2015

Keywords

Conformal invariance
Continuum scaling limit
Critical ising model
Euclidean field theory
FK clusters
Magnetization field
Planar ising model

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/13-AOP881

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keywords = "Conformal invariance, Continuum scaling limit, Critical ising model, Euclidean field theory, FK clusters, Magnetization field, Planar ising model",

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AB - The aim of this paper is to prove the following result. Consider the critical Ising model on the rescaled grid aZ2, then the renormalized magnetization field Φa := a15/8 ∑ x∈aZ2 σxδx, seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size a ↓ 0. The limiting field is conformally covariant.

KW - Conformal invariance

KW - Continuum scaling limit

KW - Critical ising model

KW - Euclidean field theory

KW - FK clusters

KW - Magnetization field

KW - Planar ising model

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Planar ising magnetization field I. uniqueness of the critical scaling limit

Abstract

Keywords

ASJC Scopus subject areas

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