Planar Ising magnetization field I. Uniqueness of the critical scaling limit

• Camia, Federico ^[1] ; Garban, Christophe ^[2] ; Newman, Charles M. ^[3]
  1. [1] VU University Amsterdam

     VU University Amsterdam

     Países Bajos

     
  2. [2] ENS Lyon
  3. [3] University of California (Irvine)

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 2, 2015, págs. 528-571
• Idioma: inglés
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  • 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∈aZ2σxδx, 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.