Ising spin glass in a random network with a gaussian random field

TL;DR

This paper explores phase transitions in a spin glass model with a Gaussian random field on a random network, highlighting how connectivity influences the stability of solutions and revealing differences from mean-field predictions.

Contribution

It introduces a random network model for the Ising spin glass with Gaussian random fields, analyzing replica symmetry stability as a function of connectivity.

Findings

Stable RS solution at zero temperature for small connectivity and high magnetic field.

Differences from fully connected theory in RF and SG crossover behavior.

Connectivity affects phase transition properties and solution stability.

Abstract

We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable parameter in our theory, allowing us to answer what the differences are between this description and the mean-field theory i.e., the fully connected theory. We have considered the random network random field Ising model where the spin exchange interaction as well as the RF are random variables following a Gaussian distribution. The results were found within the replica symmetric (RS) approximation, whose stability is obtained using the two-replica method. This also puts our work in the context of a broader discussion, which is the RS stability as a function of the connectivity. In particular, our results show that for small connectivity there is a region at zero temperature where the RS solution remains stable above a given value of the magnetic field no matter the strength of RF. Consequently, our results show important differences with the crossover between the RF and SG regimes predicted by the fully connected theory.