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

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

2004-09-03

arxiv.org/abs/math/0409046v1

Mathematics

Probability

17 pages

Scientific paper

In 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.\

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