An Analysis of Ising Type Models On Cayley Tree by a Contour Argument

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dc.creatorRozikov, U. A.
dc.date2004-09-03
dc.date.accessioned2026-07-07T05:11:46Z
dc.date.available2026-07-07T05:11:46Z
dc.descriptionIn the paper the Ising model with competing $J_1$ and $J_2$ interactions with spin values $\pm 1$, on a Cayley tree of order 2 (with 3 neighbors) is considered . We study the structure of the ground states and verify the Peierls condition for the model. Our second result gives description of Gibbs measures for ferromagnetic Ising model with $J_1<0$ and $J_2=0$, using a contour argument which we also develop in the paper. By the argument we also study Gibbs measures for a natural generalization of the Ising model. We discuss some open problems and state several conjectures.\
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0409046
dc.identifierhttp://arxiv.org/abs/math/0409046
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72354
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35; 82B05;82B20
dc.titleAn Analysis of Ising Type Models On Cayley Tree by a Contour Argument
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