Phase Transition and Critical Values of a Nearest-Neighbor System with Uncountable Local State Space on Cayley Trees View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2014-12-01

AUTHORS

Benedikt Jahnel, Christof Külske, Golibjon I. Botirov

ABSTRACT

We consider a ferromagnetic nearest-neighbor model on a Cayley tree of degree k≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$k\geqslant 2$\end{document} with uncountable local state space [0,1] where the energy function depends on a parameter 𝜃 ∈[0, 1). We show that for 0≤𝜃≤53k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0\leqslant \theta \leqslant \frac {5}{3k}$\end{document} the model has a unique translation-invariant Gibbs measure. If 53k<𝜃<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac {5}{3k}<\theta <1$\end{document} there is a phase transition, in particular there are three translation-invariant Gibbs measures. More... »

PAGES

323-331

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11040-014-9158-1

DOI

http://dx.doi.org/10.1007/s11040-014-9158-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020064246


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