p>2 spin glasses with first order ferromagnetic transitions

TL;DR

This paper investigates an infinite-range spherical p-spin glass model with added r-spin ferromagnetic interactions, revealing first order ferromagnetic transitions and different phases depending on the relation between r and p.

Contribution

It introduces a combined static and dynamic analysis of the model, showing the existence of multiple ferromagnetic phases and phase transition types based on r and p values.

Findings

First order ferromagnetic transitions for r>2

Two ferromagnetic phases for r<p, including glassy and non-glassy

Only replica symmetric phase exists for r>=p

Abstract

We consider an infinite-range spherical p-spin glass model with an additional r-spin ferromagnetic interaction, both statically using a replica analysis and dynamically via a generating functional method. For r>2 we find that there are first order transitions to ferromagnetic phases. For r<p there are two ferromagnetic phases, one non-glassy replica symmetric and one exhibiting glassy one-step replica symmetry breaking and aging, whereas for r>=p only the replica symmetric phase exists.