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

Federico Camia, Christophe Garban, Charles M. Newman

Research output: Contribution to journalArticlepeer-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 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 - 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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