The description of generalized translation-invariant $p$-adic

M. Alp   ; Chin Hee Pah   ; M. K. Saburov

Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 3, pp. 469-485

Résumé

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 $\mathbb{Q}_p$.

Détail

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

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