Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2012-08-11

AUTHORS

Yu. Kh. Eshkabilov, F. H. Haydarov, U. A. Rozikov

ABSTRACT

We consider models with nearest-neighbor interactions and with the set [0, 1] of spin values, on a Cayley tree of order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$k\geqslant 1$\end{document}. It is known that the ‘splitting Gibbs measures’ of the model can be described by solutions of a nonlinear integral equation. For arbitrary \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} we find a sufficient condition under which the integral equation has unique solution, hence under the condition the corresponding model has unique splitting Gibbs measure. More... »

PAGES

1-17

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11040-012-9118-6

DOI

http://dx.doi.org/10.1007/s11040-012-9118-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1034464484


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