New Phase transitions of the Ising model on Cayley trees

TL;DR

This paper reveals new temperature-driven phase transitions in the Ising model on Cayley trees, characterized by changes in Gibbs states and free energy behavior at multiple inverse temperatures.

Contribution

It introduces previously unknown phase transitions occurring at various inverse temperatures, beyond the critical point, in the Ising model on Cayley trees.

Findings

Multiple new phase transition points identified.

Changes in the number of Gibbs states at these points.

Significant shifts in free energy behavior.

Abstract

We show that the nearest neighbors Ising model on the Cayley tree exhibits new temperature driven phase transitions. These transitions holds at various inverse temperatures different from the critical one. They are depicted by a change in the number of Gibbs states as well as by a drastic change of the behavior of free energies at these new transition points.