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

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.

arXiv comment10 pages, 3 figures, 1 table

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Cited by in corpus (8)

• Rare behavior of growth processes via umbrella sampling of trajectories
• Large deviations in models of growing clusters with symmetry-breaking transitions
• Similarity of ensembles of trajectories of reversible and irreversible growth processes
• Effects of population growth on the success of invading mutants
• Varied phenomenology of models displaying dynamical large-deviation singularities
• The statistics of fixation times for systems with recruitment
• Fixation in Fluctuating Populations
• Balancing conservative and disruptive growth in the voter model