Self-sustained Clusters and Ergodicity Breaking in Spin Models

TL;DR

This paper investigates the formation of self-sustained clusters and ergodicity breaking in fully connected Ising and SK models, revealing new phenomena and phase transitions in cluster behavior across different regimes.

Contribution

It introduces a novel analysis of clustering and ergodicity breaking in spin models, uncovering phenomena not previously observed and suggesting applicability to other models.

Findings

No non-trivial clusters in Ising ferromagnetic and paramagnetic regimes

Restricted spin clusters in SK spin glass

First order phase transition in SK ferromagnet clusters

Abstract

The emergence of self-sustained clusters and their role in ergodicity breaking is investigated in fully connected Ising and Sherrington-Kirkpatick (SK) models. The analysis reveals a clustering behavior at various parameter regimes, as well as yet unobserved phenomena such as the absence of non-trivial clusters in the Ising ferromagnetic and paramagnetic regimes, the formation of restricted spin clusters in SK spin glass and a first order phase transition in cluster sizes in the SK ferromagnet. The method could be adapted to investigate other spin models.