Frustrated Blume-Emery-Griffiths model

TL;DR

This paper analyzes a generalized spin glass model with complex interactions, revealing a richer phase diagram with first and second order transitions, including phase separation, and examines the stability of replica symmetry.

Contribution

It introduces a generalized Blume-Emery-Griffiths model with disorder and quadrupolar interactions, providing new insights into phase transitions and stability analysis.

Findings

First order transition persists with disorder

Rich phase diagram with multiple transition types

Analytical and numerical transition line determination

Abstract

A generalised integer S Ising spin glass model is analysed using the replica formalism. The bilinear couplings are assumed to have a Gaussian distribution with ferromagnetic mean <J_ij> = Jo. Incorporation of a quadrupolar interaction term and a chemical potential leads to a richer phase diagram with transitions of first and second order. The first order transition may be interpreted as a phase separation, and contrary to what has been argued previously, it persists in the presence of disorder. Finally, the stability of the replica symmetric solution with respect to fluctuations in replica space is analysed, and the transition lines are obtained both analytically and numerically.