On the dynamical behavior of the ABC model
  We consider the ABC dynamics, with equal density of the three species, on the discrete ring with $N$ sites. In this case, the process is reversible with respect to a Gibbs measure with a mean field interaction that undergoes a second order phase transition. We analyze the relaxation time of the dynamics and show that at high temperature it grows at most as $N^2$ while it grows at least as $N^3$ at low temperature. 
L. Bertini, N. Cancrini, G. Posta
math.PR cond-mat.stat-mech