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$$p$$-Adic Quasi Gibbs Measures for the Three-State SOS Model with an External Field on a Cayley Tree

M. M. RahmatullaevNamangan State University, 161, Boburshokh str., Namangan, 160107, UzbekistanO. U. AkhmedovFerghana State University, 19, Murabbiylar str., Ferghana, 150100, Uzbekistan

P-Adic Numbers Ultrametric Analysis and Applicationsjournal2026en

ABI

Annotatsiya

We consider a three-state solid-on-solid (SOS) model in the presence of a nonzero external field on a Cayley tree. A system of functional equations corresponding to this model is derived, where each solution defines a quasi Gibbs measure. Based on this system, we investigate the translation-invariant $$p$$ -adic quasi Gibbs measures (TIpQGMs) of the model. In the case of a binary Cayley tree, we explicitly determine the TIpQGMs under the same conditions. Furthermore, by analyzing the boundedness of these measures, we establish the existence of a phase transition.

Mavzular

advanced mathematical theories Mathematical Dynamics and Fractals Stochastic processes and statistical mechanics

Identifikatorlar

DOI: 10.1134/s2070046626020056

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