Phase transitions for a model with uncountable spin space on the Cayley tree: The general case
dc.bibliographicCitation.volume | 2490 | |
dc.contributor.author | Botirov, Golibjon | |
dc.contributor.author | Jahnel, Benedikt | |
dc.date.accessioned | 2018-04-16T09:57:59Z | |
dc.date.available | 2019-06-28T08:17:13Z | |
dc.date.issued | 2018 | |
dc.description.abstract | In this paper we complete the analysis of a statistical mechanics model on Cayley trees of any degree, started in [EsHaRo12, EsRo10, BoEsRo13, JaKuBo14, Bo17]. 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 θ c such that for θ≤θ c there is a unique translation-invariant splitting Gibbs measure. For θ c < 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. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2986 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3115 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2490 | |
dc.relation.ispartofseries | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2490, ISSN 2198-5855 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject | Cayley trees | eng |
dc.subject | Hammerstein operators | eng |
dc.subject | splitting Gibbs measures | eng |
dc.subject | phase transitions | eng |
dc.subject.ddc | 510 | eng |
dc.title | Phase transitions for a model with uncountable spin space on the Cayley tree: The general case | eng |
dc.type | report | eng |
dc.type | Text | eng |
dcterms.bibliographicCitation.journalTitle | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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