Phase transitions for a model with uncountable spin space on the Cayley tree: the general case View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-04

AUTHORS

Golibjon Botirov, Benedikt Jahnel

ABSTRACT

In this paper we complete the analysis of a statistical mechanics model on Cayley trees of any degree, started in Botirov (Positivity 21(3):955–961, 2017), Eshkabilov et al. (J Stat Phys 147(4):779–794, 2012), Eshkabilov and Rozikov (Math Phys Anal Geom 13:275–286, 2010), Botirov et al. (Lobachevskii J Math 34(3):256–263 2013) and Jahnel et al. (Math Phys Anal Geom 17:323–331 2014). The potential is of nearest-neighbor type and the local state space is compact but uncountable. Based on the system parameters we prove existence of a critical value θc such that for θ≤θc there is a unique translation-invariant splitting Gibbs measure. For θc<θ there is a phase transition with exactly three translation-invariant splitting Gibbs measures. The proof rests on an analysis of fixed points of an associated non-linear Hammerstein integral operator for the boundary laws. More... »

PAGES

291-301

Journal

TITLE

Positivity

ISSUE

2

VOLUME

23

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11117-018-0606-1

DOI

http://dx.doi.org/10.1007/s11117-018-0606-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1106195896


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