# Phase transition for models with continuum set of spin values on Bethe lattice

## TL;DR

This paper analyzes models with a continuum of spin values on a Bethe lattice, characterizing all Gibbs measures and exploring phase transitions depending on a parameter.

## Contribution

It provides a complete description of Gibbs measures for models with continuum spins on Bethe lattices, revealing phase transition phenomena.

## Key findings

- Characterization of all Gibbs measures for the models.
- Identification of phase transition points depending on parameter θ.
- Analysis applicable to Bethe lattices of arbitrary order.

## Abstract

In this paper we consider models with nearest-neighbor interactions and with the set [0,1] of spin values, on a Bethe lattice (Cayley tree) of an arbitrary order. These models depend on parameter $\theta$. We describe all of Gibbs measures in any right parameter $\theta$ corresponding to the models.