Geodesic
Translation-invariant $p$-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 1, pp. 155-176 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the $p$-adic Ising–Vannimenus model on the Cayley tree of order $k=2$. This model contains nearest-neighbor and next-nearest-neighbor interactions. We investigate the model using a new approach based on measure theory (in the $p$-adic sense) and describe all translation-invariant $p$-adic quasi-Gibbs measures associated with the model. As a consequence, we can prove that a phase transition exists in the model. Here, "phase transition" means that there exist at least two nontrivial $p$-adic quasi-Gibbs measures such that one is bounded and the other is unbounded. The methods used are inapplicable in the real case.
Keywords: $p$-adic numbers, Ising–Vannimenus model, $p$-adic Gibbs measure, dynamical system, Cayley tree.
Mots-clés : phase transition 
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     title = {Translation-invariant $p$-adic {quasi-Gibbs} measures for {the~Ising{\textendash}Vannimenus} model on {a~Cayley} tree},
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F. M. Mukhamedov; M. Kh. Saburov; O. N. Khakimov. Translation-invariant $p$-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 1, pp. 155-176. http://geodesic.mathdoc.fr/item/TMF_2016_187_1_a11/

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