Phase Transitions for a model with uncountable set of spin values on a Cayley tree

Yu. Kh. Eshkabilov, U. A. Rozikov, G. I. Botirov

Published 2012-10-27Version 1

In this paper we consider a model with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k \geq 2$. To study translation-invariant Gibbs measures of the model we drive an nonlinear functional equation. For $k=2$ and 3 under some conditions on parameters of the model we prove non-uniqueness of translation-invariant Gibbs measures (i.e. there are phase transitions).