Phase diagrams of soluble multi-spin glass models

TL;DR

This paper explores the phase diagrams of soluble multi-spin glass models with p-spin interactions, revealing first-order transitions and the absence of stable mixed phases when ferromagnetic interactions are present.

Contribution

It introduces a simplified, replica-free solution for a spherical spin-glass model with p-spin interactions, enabling detailed analysis of phase transitions.

Findings

First-order transitions occur for p ≥ 3.

No stable mixed phase with both ferromagnetic and spin-glass properties.

Detailed phase diagrams of the model are provided.

Abstract

We include p-spin interactions in a spherical version of a soluble mean-field spin-glass model proposed by van Hemmen. Due to the simplicity of the solutions, which do not require the use of the replica trick, we are able to carry out a detailed investigation of a number of special situations. For p larger or equal to 3, there appear first-order transitions between the paramagnetic and the ordered phases. In the presence of additional ferromagnetic interactions, we show that there is no stable mixed phase, with both ferromagnetic and spin-glass properties.