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Crossover behaviour of a one dimensional Random Energy Model

Matteo Campellone·Silvio Franz·Giorgio Parisi
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Abstract

In this note we formulate a finite dimensional generalization of the Random Energy Model (REM) where we introduce a geometry and spatial correlations between energies. We study the model in dimension one by transfer matrix techniques and we look at the crossover from one dimensional to mean-field behaviour. In a first version of the model the mean field limit reproduces the behaviour of the original REM, while a second version of the model exhibits a first order phase transition with a finite latent heat.

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Matteo Campellone, Silvio Franz, Giorgio Parisi. 1998-03-11. Crossover behaviour of a one dimensional Random Energy Model. https://doi.org/10.1103/physreve.58.5455

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