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Fast Mixing for the Low Temperature 2D Ising Model Through Irreversible Parallel Dynamics

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Abstract

We study tunneling and mixing time for a non-reversible probabilistic cellular automaton. With a suitable choice of the parameters, we first show that the stationary distribution is close in total variation to a low temperature Ising model. Then we prove that both the mixing time and the time to exit a metastable state grow polynomially in the size of the system, while this growth is exponential in reversible dynamics. In this model, non-reversibility, parallel updatings and a suitable choice of boundary conditions combine to produce an efficient dynamical stability.

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Authors and Affiliations

  1. Dipartimento di Matematica, University of Padova, Via Trieste 63, 35121, Padua, Italy

    Paolo Dai Pra

  2. Dipartimento di Matematica, University of Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133, Roma, Italy

    Benedetto Scoppola

  3. Dipartimento di Matematica e Fisica, University of Roma “Roma Tre”, Largo San Murialdo, 1, 00146, Roma, Italy

    Elisabetta Scoppola

Authors
  1. Paolo Dai Pra
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  2. Benedetto Scoppola
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  3. Elisabetta Scoppola
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Correspondence to Paolo Dai Pra.

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Dai Pra, P., Scoppola, B. & Scoppola, E. Fast Mixing for the Low Temperature 2D Ising Model Through Irreversible Parallel Dynamics. J Stat Phys 159, 1–20 (2015). https://doi.org/10.1007/s10955-014-1180-y

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  • DOI: https://doi.org/10.1007/s10955-014-1180-y

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