Surface order large deviations for Ising, Potts and percolation models
type: Item
instance of: scholarly article
title: Surface order large deviations for Ising, Potts and percolation models
zbMATH Open document ID: 0842.60022
DOI: 10.1007/BF01198161
author: Ágoston Pisztora
publication date: 1996-07-22T00:00:00Z
review text: We derive uniform surface order large deviation estimates for the block magnetization in finite volume Ising (or Potts) models with plus or free (or a combination of both) boundary conditions in the phase coexistence regime for \(d\geq 3\). The results are valid up to a limit of slab-thresholds, conjectured to agree with the critical temperature. Our arguments are based on the renormalization of the random cluster model with \(q\geq 1\) and \(d\geq 3\), and on corresponding large deviation estimates for the occurrence in a box of the largest cluster with density close to the percolation probability. The results are new even for the case of independent percolation \((q=1)\). As a byproduct of our methods, we obtain further results in the FK model concerning semicontinuity (in \(p\) and \(q\)) of the percolation probability, the second largest cluster in a box and the tail of the finite cluster size distribution.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 82B43
zbMATH DE Number: 878013
zbMATH Keywords: large deviation estimates
zbMATH Keywords: phase coexistence regime
zbMATH Keywords: percolation probability
zbMATH Keywords: cluster size distribution
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01198161
OpenAlex ID: W2073921960
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 878013