Ergodicity and Mixing Properties of the Northeast Model

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dc.creatorKordzakhia, George
dc.creatorLalley, Steven P.
dc.date2006-01-09
dc.date.accessioned2026-07-07T06:58:38Z
dc.date.available2026-07-07T06:58:38Z
dc.descriptionThe 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 $p<p_{c}$, the trivial measure $δ_{0}$ that puts mass one on the configuration with all spins set at $0$ is the unique ergodic, translation invariant, stationary measure. For $p\geq p_{c}$, the product Bernoulli-$p$ measure on configuration space is the unique nontrivial, ergodic, translation invariant, stationary measure for the system, and it is mixing. For $p>2/3$ it is shown that there is exponential decay of correlations.
dc.identifierhttps://arxiv.org/abs/math/0601157
dc.identifierhttp://arxiv.org/abs/math/0601157
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107437
dc.subjectProbability
dc.subject60J25, 60K35
dc.titleErgodicity and Mixing Properties of the Northeast Model
dc.typetext

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