Exact phase diagrams for an Ising model on a two-layer Bethe lattice

TL;DR

This paper derives exact phase diagrams for a two-layer Bethe lattice Ising model with different intralayer and interlayer couplings, external fields, and provides precise thermodynamic expressions.

Contribution

It introduces an iteration technique to obtain exact free energy and magnetization expressions for a layered Bethe lattice Ising model with variable couplings and external fields.

Findings

Exact phase diagrams for the two-layer Bethe lattice system.

Closed-form expressions for free energy and magnetization.

Insights into the effects of interlayer and intralayer couplings.

Abstract

Using an iteration technique, we obtain exact expressions for the free energy and the magnetization of an Ising model on a two - layer Bethe lattice with intralayer coupling constants J1 and J2 for the first and the second layer, respectively, and interlayer coupling constant J3 between the two layers; the Ising spins also couple with external magnetic fields, which are different in the two layers. We obtain exact phase diagrams for the system.