Growth-induced breaking and unbreaking of ergodicity in fully-connected spin systems

TL;DR

This paper investigates how growth processes in fully-connected spin systems like voter and Glauber-Ising models can fundamentally change their long-term ergodic properties, either breaking or restoring ergodicity.

Contribution

It introduces growth modifications to classical models and analyzes their impact on ergodicity in regimes where growth and internal dynamics are intertwined.

Findings

Growth can break ergodicity in some models.

Growth can unbreak ergodicity in others.

Long-term behavior is highly sensitive to growth mechanisms.

Abstract

Two canonical models of statistical mechanics, the fully-connected voter and Glauber-Ising models, are modified to incorporate growth via the addition or replication of spins. The resulting behaviour is examined in a regime where the timescale of expansion cannot be separated from that of the internal dynamics. Depending on the model specification, growth radically alters the long-time dynamical behaviour by breaking or unbreaking ergodicity.