Phase transitions for models with a continuum set of spin values on a Bethe lattice

Abstract

We consider a model with nearest-neighbor interactions and the set $$[0,1]$$ of spin values on a Bethe lattice (Cayley tree) of arbitrary order. This model depends on a continuous parameter $$\theta$$ and is a generalization of known models. For all values of $$\theta$$ , we give a complete description of the set of translation-invariant Gibbs measures of this model.