Abstract
We consider a three-state solid-on-solid (SOS) model on a Cayley tree in the presence of an external field. We show that periodic Gibbs measures are either translation invariant or periodic with period two. We describe two-periodic Gibbs measures of the model.
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Acknowledgments
The author is greatly indebted to Professors U. A. Rozikov and M. M. Rahmatullaev for suggesting the problem and for many stimulating conversations.
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 212, pp. 448–456 https://doi.org/10.4213/tmf10280.
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Karshiboev, O.S. Periodic Gibbs measures for the three-state SOS model on a Cayley tree with a translation-invariant external field. Theor Math Phys 212, 1276–1283 (2022). https://doi.org/10.1134/S0040577922090094
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DOI: https://doi.org/10.1134/S0040577922090094