Spin-1 Hopfield model under a random field

Abstract

The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three state Hopfield model under a Gaussian Random Field. In order to control the nontrivial disorder, the Hebb interaction is used. It provides a way to control the system frustration by means of the parameter a = p N , varying from trivial randomness to a highly frustrated regime, in the thermodynamic limit. We performed the thermodynamic analysis using the one-step replicasymmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of a, anisotropy constant and the Random Field.