We demonstrate existence and boundedness of p-adic quasi-Gibbs measures in a three-state SOS model, indicating potential phase transitions.
In this paper, we study p-adic quasi-Gibbs measures for the three-state SOS model on a Cayley tree of order two. The existence of new translation-invariant p-adic quasi-Gibbs measures have been found. Moreover, the boundedness of the found translation-invariant p-adic quasi-Gibbs measures is proven. Furthermore, we show if (θₛ/p)=1, s is even and p≡ 1 (mod6), then a phase transition occurs.
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Akhmedov O.U. (2025) studied this question.
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