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.
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Morris et al. (2014) studied this question.
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