Abstract
We consider a p-adic Ising model on the Cayley tree of order k ≥ 2. We completely describe all p-adic-translation-invariant generalized Gibbs measures for k = 3. Moreover, we show the existence of a phase transition for the p-adic Ising model for any k ≥ 3 if p ≡ 1 (mod 4).
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The authors thank Professor U. A. Rozikov for the useful discussions. Conflicts of interest. The authors declare no conflicts of interest.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 201, No. 1, pp. 126–136, October, 2019.
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Rahmatullaev, M.M., Khakimov, O.N. & Tukhtaboev, A.M. A p-Adic Generalized Gibbs Measure for the Ising Model on a Cayley Tree. Theor Math Phys 201, 1521–1530 (2019). https://doi.org/10.1134/S004057791910009X
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DOI: https://doi.org/10.1134/S004057791910009X