Stability of the Phase Transition of Critical-Field Ising Model on Cayley trees under Inhomogeneous External Fields

TL;DR

This paper studies the phase transition behavior of the ferromagnetic Ising model on Cayley trees with spatially varying external fields, identifying conditions under which phase transitions occur, extending previous research.

Contribution

It extends earlier results by Rozikov and Ganikhodjaev to include inhomogeneous external fields approaching a critical value.

Findings

Identifies conditions for phase transition existence under inhomogeneous fields

Extends prior results to more general external field configurations

Provides theoretical criteria for phase transition stability

Abstract

We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for a class of external fields, asymptotically approaching a homogeneous critical external field. Our results extend earlier results by Rozikov and Ganikhodjaev.