On the Generalised Random Energy Model

Dorlas, T. C. and Dukes, W.M.B. (2001) On the Generalised Random Energy Model. (Preprint)

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Abstract

The Generalised Random Energy Model is a generalisation of the Random Energy Model introduced by Derrida to mimic the ultrametric structure of the Parisi solution of the Sherrington-Kirkpatrick model of a spin glass. It was solved exactly in two special cases by Derrida and Gardner. A rigorous analysis by Capocaccia et al. claimed to give a complete solution for the thermodynamics of the model in the general case. Here we use Large Deviation Theory to analyse the model along the lines followed by Dorlas and Wedagedera for the Random Energy Model. The resulting variational expression for the free energy is the same as that found by Capocaccia et al. We show that it can be evaluated in a very simple way. We find that the answer given by Capocaccia et al. is incorrect.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 13 Jun 2018 13:08
Last Modified: 17 Jul 2018 11:47
URI: http://dair.dias.ie/id/eprint/441

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