Replica analysis of the p-spin interactions Ising spin-glass model

TL;DR

This paper analytically investigates the thermodynamics of the infinite-range p-spin Ising spin-glass model under an external magnetic field, focusing on the transition between replica symmetric and one-step replica symmetry breaking regimes.

Contribution

It provides analytical conditions for the continuous transition onset and the tricritical point where the transition becomes discontinuous.

Findings

Derived conditions for the continuous transition

Identified the tricritical point location

Analyzed the transition between symmetry regimes

Abstract

The thermodynamics of the infinite-range Ising spin glass with p-spin interactions in the presence of an external magnetic field h is investigated analytically using the replica method. We give emphasis to the analysis of the transition between the replica symmetric and the one-step replica symmetry breaking regimes. In particular, we derive analytical conditions for the onset of the continuous transition, as well as for the location of the tricritical point at which the transition between those two regimes becomes discontinuous.