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arXiv · 1401.8010

Spin-1 Hopfield model under a random field

C. V. Morais·M. J. Lazo·F. M. Zimmer·P. R. Krebs·S. G. Magalhaes
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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. This 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 replica-symmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of a, the anisotropy constant, and the random field.

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C. V. Morais, M. J. Lazo, F. M. Zimmer, P. R. Krebs, S. G. Magalhaes. 2014-01-30. Spin-1 Hopfield model under a random field. https://doi.org/10.1103/physreve.89.012146

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