Spin-glass behaviour on random lattices

TL;DR

This paper investigates the phase diagram of an Ising spin-glass model on random graphs with varying ferromagnetic interaction fractions, revealing a critical point at equal ferromagnetic and antiferromagnetic interactions that separates different magnetic phases.

Contribution

It provides a detailed analysis of the ground-state phase diagram of a spin-glass model on random lattices using the replica method, highlighting the significance of the unbiased case at w=1/2.

Findings

w=1/2 is a singular point in the phase diagram

Different phases are separated by this critical point

The phase diagram includes spin-glass, ferromagnetic, mixed, and paramagnetic phases

Abstract

The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction $w$ of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that $w=1/2$, correponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase ($w<1/2$) from a region with spin-glass, ferromagnetic, mixed, and paramagnetic phases ($w>1/2$).