Total spin asymptotic normality at the critical point for a classical statistical physics model
type: Item
instance of: scholarly article
title: Total spin asymptotic normality at the critical point for a classical statistical physics model
zbMATH Open document ID: 0910.60009
author: S. H. Smith
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 1998-11-05T00:00:00Z
review text: It is presented a lattice model with a Hamiltonian given by the formula \[ H_\Lambda^{\beta,h} (x/ \overline x) ={\beta\over 2} \sum_{t,s\in \Lambda, \|t-s\|=1} |x_t||x_s|+ \beta\sum_{t\in \Lambda, s\in \partial\Lambda} |x_t| |\overline x_s| +h\sum_{t\in \Lambda} |x_t|, \] \(x_t,x_s\in X=\{-1,0,1\},\) \(t,s\in Z^\nu\), \(h\in R^1\), \(\beta>0\), \(x\in X^\Lambda\), \(\overline x\in X^{\partial \Lambda}\). It is shown that in this model there is a phase transition on the line \(h+\beta \nu-\ln 2=0\) and that the total spin at the critical point has non-standard behaviour, i.e. the central limit theorem is valid.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 1190936
zbMATH Keywords: central limit theorem
zbMATH Keywords: Ising model
zbMATH Keywords: total spin
zbMATH Keywords: lattice model
zbMATH Keywords: phase transition
reviewed by: S. Poghosyan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1190936