Global Bethe lattice consideration of the spin-1 Ising model

TL;DR

This paper analyzes the spin-1 Ising model with complex interactions on the Bethe lattice, revealing detailed phase diagrams and phenomena like reentrant behavior and ferrimagnetism through exact recursion equations.

Contribution

It provides an exact solution for the spin-1 Ising model on the Bethe lattice, including comprehensive phase diagrams and analysis of critical properties for various coupling parameters.

Findings

Identification of reentrant phase transitions

Observation of ferrimagnetic phases

Comparison with other approximation methods

Abstract

The spin-1 Ising model with bilinear and biquadratic exchange interactions and single-ion crystal field is solved on the Bethe lattice using exact recursion equations. The general procedure of critical properties investigation is discussed and full set of phase diagrams are constructed for both positive and negative biquadratic couplings. In latter case we observe all remarkable features of the model, uncluding doubly-reentrant behavior and ferrimagnetic phase. A comparison with the results of other approximation schemes is done.