Three state random energy model

TL;DR

This paper introduces a spin-1 random energy model with crystal field, analyzing its phase transitions, including spin-glass and de Almeida Thouless lines, and explores its thermodynamic properties under various external conditions.

Contribution

It presents a novel spin-1 random energy model with crystal field, providing exact solutions and phase diagrams, including spin-glass transition and response to magnetic fields.

Findings

Spin-glass transition occurs at finite temperature for all crystal field strengths.

The model exhibits a de Almeida Thouless line indicating replica symmetry breaking.

Magnetization shows non-monotonic behavior at high positive crystal fields.

Abstract

We introduce a spin-1 version of the random energy model with crystal field. Crystal field controls the density of 0 spins in the system. We solve the model in the micro-canonincal ensemble. The model has a spin-glass transition at a finite temperature for all strengths of the crystal field. By introducing the magnetic field we also obtain the de Almeida Thouless line for the model. The spin-glass transition persists in the presence of external field. We also find that the magnetisation shows non-monotonic behaviour for high positive crystal field strengths. The zero magnetic field specific heat and magnetic susceptibility also exhibit a cusp beyond a threshold value of the crystal field.