Phase Transitions for a model with uncountable set of spin values on a   Cayley tree
  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). 
Yu. Kh. Eshkabilov, U. A. Rozikov, G.I. Botirov
math-ph math.MP