Mean Field Spin Glass in the Observable Representation

TL;DR

This paper presents a novel low-dimensional embedding of the mean field SK spin glass state space, enabling visualization and analysis of metastable and stable phases, their relationships, and features like the Parisi overlap distribution.

Contribution

It introduces a new observable representation that embeds the high-dimensional state space into a low-dimensional space, revealing phase structure and dynamics.

Findings

Metastable and stable phases can be distinguished visually.

Peaks in the Parisi overlap distribution are identifiable.

Hierarchical relations among phases are directly observable.

Abstract

The state space for the $N$-spin mean field (SK) spin glass--nominally an $N$-cube--is embedded in a low dimensional continuous space in such a way that metastable and stable phases can easily be discerned, a concept of nearness of configurations defined, and peaks in the Parisi $q$-parameter overlap distribution identified. The dynamical and partly hierarchical interrelation of these phases can be directly imaged.