M. Alp, Chin Hee Pah, M. K. Saburov, “The description of generalized translation-invariant <nobr>$p$</nobr>-adic Gibbs measures for the Potts model on the Cayley tree of order three”, TMF, 2023, Volume 214, Number 3,Pages <nobr>469

This article is cited in 1 paper

The description of generalized translation-invariant $p$-adic Gibbs measures for the Potts model on the Cayley tree of order three

M. Alp^a, Chin Hee Pah^b, M. K. Saburov^a

^a College of Engineering and Technology, American University of the Middle East, Kuwait City, Kuwait
^b Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, Pahang, Kuantan, Malaysia

Abstract: We describe generalized translation-invariant $p$-adic Gibbs measures for the Potts model on the Cayley tree of order three, confirming and extending the related results in the literature. We introduce a cube root function over the $p$-adic field $\mathbb{Q}_p$, which enables us to explicitly prescribe all roots of the cubic monomial equation over $\mathbb{Q}_p$.

Keywords: Gibbs measure, Potts model, Cayley tree, $p$-adic field.

MSC: 82B26, 46S10, 12J12, 39A70, 47H10, 60K35

Received: 18.09.2022
Revised: 15.10.2022

DOI: 10.4213/tmf10376