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Ergodicity and Mixing Properties of the Northeast Model

George Kordzakhia·Steven P. Lalley
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Abstract

The Northeast Model is a spin system on the two-dimensional integer lattice that evolves according to the following rule: Whenever a site's southerly and westerly nearest neighbors have spin $1$, it may reset its own spin by tossing a $p$-coin; at all other times, its spin remains frozen. It is proved that the northeast model has a phase transition at $p_{c}=1-β_{c}$, where $β_{c}$ is the critical parameter for oriented percolation. For $p 2/3$ it is shown that there is exponential decay of correlations.

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George Kordzakhia, Steven P. Lalley. 2006-01-09. Ergodicity and Mixing Properties of the Northeast Model. https://arxiv.org/abs/math/0601157

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