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.
On the Dynamical Behavior of the ABC Model / BERTINI MALGARINI, Lorenzo; Nicoletta, Cancrini; Posta, Gustavo. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 144:6(2011), pp. 1284-1307. [10.1007/s10955-011-0294-8]