Growth-induced breaking and unbreaking of ergodicity in fully-connected   spin systems
  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. 
Richard G. Morris and Tim Rogers
cond-mat.stat-mech