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

摘要

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.