O‘zbekiston matematika jurnali Том 69 № 3 (2025) · с. 5-14
p-adic quasi-Gibbs measures for the three-state SOS model on the binary tree
Akhmedov O.U.
Аннотация
In this paper, we study $p$-adic quasi-Gibbs measures forthe three-state SOS model on a Cayley tree of order two. The existence ofnew 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 $\left(\frac{\theta_s}{p}\right)=1$, $s$ is even and $p\equiv 1 (\operatorname{mod}6)$,then a phase transition occurs.
Cayley tree, configuration, p-adic numbers, p-adic SOS model, p-adic quasi-Gibbs measure, periodic measure
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