On the dynamical behavior of the ABC model

Details On the dynamical behavior of the ABC model On the dynamical behavior of the ABC model

2011-04-05

arxiv.org/abs/1104.0822v2

Mathematics

Probability

Scientific paper

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.

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