Fast mixing for the low temperature 2d Ising model through irreversible parallel dynamics

Paolo Dai Pra; Benedetto Scoppola; Elisabetta Scoppola

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arXiv · 1407.6650

Fast mixing for the low temperature 2d Ising model through irreversible parallel dynamics

Paolo Dai Pra·Benedetto Scoppola·Elisabetta Scoppola

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Abstract

We study metastability 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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Paolo Dai Pra, Benedetto Scoppola, Elisabetta Scoppola. 2014-07-24. Fast mixing for the low temperature 2d Ising model through irreversible parallel dynamics. https://arxiv.org/abs/1407.6650

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