Phase transitions for a model with uncountable spin space on the Cayley\n tree: the general case

In this paper we complete the analysis of a statistical mechanics model on\nCayley trees of any degree, started in\n[EsHaRo12,EsRo10,BoEsRo13,JaKuBo14,Bo17]. The potential is of nearest-neighbor\ntype and the local state space is compact but uncountable. Based on the system\nparameters we prove existence of a critical value $\\theta_{\\rm c}$ such that\nfor $\\theta\\le \\theta_{\\rm c}$ there is a unique translation-invariant\nsplitting Gibbs measure. For $\\theta_{\\rm c}<\\theta$ there is a phase\ntransition with exactly three translation-invariant splitting Gibbs measures.\nThe proof rests on an analysis of fixed points of an associated non-linear\nHammerstein integral operator for the boundary laws.\n

Перевод пока недоступен