p-adic quasi-Gibbs measures for the three-state SOS model on the binary tree

Authors

  • Akhmedov O.U. Author

DOI:

https://doi.org/10.29229/uzmj.2025-3-1

Keywords:

Cayley tree, configuration, p-adic numbers, p-adic SOS model, p-adic quasi-Gibbs measure, periodic measure

Abstract

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 $\left(\frac{\theta_s}{p}\right)=1$, $s$ is even and $p\equiv 1 (\operatorname{mod}6)$,
then a phase transition occurs.

Published

2025-09-06

Issue

Vol. 69 No. 3 (2025): Uzbek Mathematical Journal

Section

Articles

How to Cite

p-adic quasi-Gibbs measures for the three-state SOS model on the binary tree. (2025). Uzbek Mathematical Journal, 69(3), 5-14. https://doi.org/10.29229/uzmj.2025-3-1