Geodesic
The~description of generalized translation-invariant $p$-adic
Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 3, pp. 469-485

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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. 
@article{TMF_2023_214_3_a5,
     author = {M. Alp and Chin Hee Pah and M. K. Saburov},
     title = {The~description of generalized translation-invariant $p$-adic},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {469--485},
     publisher = {mathdoc},
     volume = {214},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_214_3_a5/}
}
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M. Alp; Chin Hee Pah; M. K. Saburov. The~description of generalized translation-invariant $p$-adic. Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 3, pp. 469-485. http://geodesic.mathdoc.fr/item/TMF_2023_214_3_a5/