Abstract
We consider the Ising model with (competing) two-step interactions and spin values ± 1, on a Cayley tree of order k ≥ 1. We constructively describe ground states and verify the Peierls condition for the model. We define notion of a contour for the model on the Cayley tree. Using a contour argument we show the existence of two different Gibbs measures.
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Rozikov, U.A. A Constructive Description of Ground States and Gibbs Measures for Ising Model with Two-Step Interactions on Cayley Tree. J Stat Phys 122, 217–235 (2006). https://doi.org/10.1007/s10955-005-8029-3
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DOI: https://doi.org/10.1007/s10955-005-8029-3