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

Federico Camia, Christophe Garban, Charles M. Newman

Research output: Contribution to journalArticle

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 Φa := a15/8x∈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.

Original languageEnglish (US)
Pages (from-to)528-571
Number of pages44
JournalAnnals of Probability
Volume43
Issue number2
DOIs
StatePublished - Jan 1 2015

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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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