Ergodicity and Mixing Properties of the Northeast Model

Details Ergodicity and Mixing Properties of the Northeast Model Ergodicity and Mixing Properties of the Northeast Model

2006-01-09

arxiv.org/abs/math/0601157v1

Mathematics

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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 $p_{c}=1-\beta_{c}$, where $\beta_{c}$ is the critical parameter for oriented percolation. For $p2/3$ it is shown that there is exponential decay of correlations.

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