Diluted Generalized Random Energy Model

TL;DR

This paper introduces a diluted version of the GREM, a layered random spin model, which effectively estimates thermodynamic properties of low-dimensional spin glasses, including the Edwards-Anderson model.

Contribution

The paper presents a diluted GREM model that approximates thermodynamic properties of spin glasses, providing accurate critical dimensions and ground state energies.

Findings

Accurately predicts critical dimension of Edwards-Anderson model

Achieves 5% accuracy for 2D ground state energy

Offers a new approximation method for low-dimensional spin glasses

Abstract

We introduce a layered random spin model, equivalent to the Generalized Random Energy Model (GREM). In analogy with diluted spin systems, a diluted GREM (DGREM) is introduced.It can be applied to calculate approximately thermodynamic properties of spin glass models in low dimensions. For Edwards -Anderson model it gives correct critical dimension and 5% accuracy for ground state energy in 2d.