Zero temperature phase diagram of finite connectivity spin glasses

TL;DR

This paper explores the zero temperature phase diagram of finite connectivity spin glasses, revealing complex behavior in mean field models and trivial phases in 3D, using analytical and numerical methods.

Contribution

It provides new analytical results on the phase diagram and reviews numerical ground state computations for finite connectivity spin glasses.

Findings

Mean field models show a complex phase diagram with a zero temperature de Almeida-Thouless line.

3D models exhibit a trivial phase diagram.

Combination of analytical and numerical approaches enhances understanding of spin glass phases.

Abstract

The zero temperature phase diagram of spin glasses on finite connectivity graphs is investigated, with or without magnetic field and/or ferromagnetic bias, for mean field (using the cavity method) and Edwards-Anderson (using numerical ground states computations) models. In the mean field case we show that the phase diagram is complex and compute the equivalent of the zero temperature de Almeida-Thouless line. In the 3d model however, we found a trivial phase diagram. This paper present new analytical results as well as a rapid review of numerical works on ground states.