Browsing by Author "Botirov, Golibjon"
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- ItemPhase transitions for a model with uncountable spin space on the Cayley tree: The general case(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Botirov, Golibjon; Jahnel, BenediktIn 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.