Random-field p-spin glass model on regular random graphs

TL;DR

This paper explores the phase diagrams of p-body +/-J Ising models on random graphs, revealing a spin glass phase in a three-body ferromagnetic model with random fields, unlike the two-body case.

Contribution

It demonstrates the existence of a thermodynamic spin glass phase in the three-body ferromagnetic model with random fields, and explains phase boundary invariance via gauge transformation.

Findings

Spin glass phase exists in three-body ferromagnetic models with random fields.

Phase boundary between paramagnetic and spin glass phases is independent of ferromagnetic bias.

Gauge invariance explains the phase boundary behavior.

Abstract

We investigate in detail the phase diagrams of the p-body +/-J Ising model with and without random fields on random graphs with fixed connectivity. One of our most interesting findings is that a thermodynamic spin glass phase is present in the three-body purely ferromagnetic model in random fields, unlike for the canonical two-body interaction random-field Ising model. We also discuss the location of the phase boundary between the paramagnetic and spin glass phases that does not depend on the change of the ferromagnetic bias. This behavior is explained by a gauge transformation, which shows that gauge-invariant properties generically do not depend on the strength of the ferromagnetic bias for the +/-J Ising model on regular random graphs.