Abstract
We introduce the notion of a weakly periodic configuration. For the Ising model with competing interactions, we describe the set of all weakly periodic ground states corresponding to normal divisors of indices 2 and 4 of the group representation of the Cayley tree. In addition, we study new Gibbs measures for the Ising model.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 3, pp. 507–516, September, 2009.
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Rozikov, U.A., Rakhmatullaev, M.M. Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree. Theor Math Phys 160, 1292–1300 (2009). https://doi.org/10.1007/s11232-009-0116-1
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DOI: https://doi.org/10.1007/s11232-009-0116-1