Magnetic proximity in a coupled Ferromagnet-Spin glass system

TL;DR

This paper investigates the interplay between ferromagnetic and spin glass phases in a coupled infinite-range Ising and Sherrington-Kirkpatrick model, revealing phase boundaries, reentrant transitions, and tricritical points through replica-symmetric analysis.

Contribution

It introduces a coupled model of ferromagnet and spin glass, providing a detailed phase diagram and stability analysis of the replica-symmetric solution.

Findings

Identification of phase boundaries similar to SK model

Reentrant transition between spin glass and ferromagnetic phases

First order transition at a tricritical point

Abstract

We study the competition between ferromagnetic and spin glass phases using a system of coupled infinite-range Ising and Sherrington-Kirkpatrick models. We obtain the replica-symmetric solution for the free energy of this system in terms of magnetization and Edwards-Anderson order parameters in both subsystems. Using these order parameters we are able to identify different phases in the system and determine which phase is dominant for different strengths of the coupling between two subsystems. We observe that both subsystems are in the same phase although with different order parameters. The phase boundary between paramagnetic-ferromagnetic and paramagnetic-spin glass phases is more or less similar to that in the Sherrington-Kirkpatrick phase diagram. But the boundary between ferromagnetic-spin glass phases becomes qualitatively different as the coupling between the two subsystems changes. Remarkably, for intermediate values of the coupling, this phase boundary is such that there could be a reentrant transition between spin glass and ferromagnetic phases by increasing the temperature. We found that for some range of the coupling, the second order transition between these phases turns into first order at a tricritical point. Further, we carry out the stability analysis by considering deviations from the replica symmetric solution.