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On the Dynamical Behavior of the ABC Model

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Abstract

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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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma ‘La Sapienza’, P.le Aldo Moro 5, 00185, Roma, Italy

    Lorenzo Bertini

  2. Dipartimento di Matematica Pura e Applicata, Università dell’Aquila, 67100, Coppito, L’Aquila, Italy

    Nicoletta Cancrini

  3. Dipartimento di Matematica, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133, Milano, Italy

    Gustavo Posta

Authors
  1. Lorenzo Bertini
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  2. Nicoletta Cancrini
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  3. Gustavo Posta
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Correspondence to Gustavo Posta.

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Bertini, L., Cancrini, N. & Posta, G. On the Dynamical Behavior of the ABC Model. J Stat Phys 144, 1284 (2011). https://doi.org/10.1007/s10955-011-0294-8

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