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On the dynamical behavior of the ABC model

By L. Bertini, N. Cancrini and G. Posta


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

Topics: Mathematics - Probability, Condensed Matter - Statistical Mechanics, Primary 60K35, 82C20, Secondary 82C22, 60B15
Year: 2011
DOI identifier: 10.1007/s10955-011-0294-8
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