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

@article{DaiPra2014FastMF,
  title={Fast Mixing for the Low Temperature 2D Ising Model Through Irreversible Parallel Dynamics},
  author={Paolo Dai Pra and Benedetto Scoppola and Elisabetta Scoppola},
  journal={Journal of Statistical Physics},
  year={2014},
  volume={159},
  pages={1-20}
}
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… Expand
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