Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree

• Main Authors: Mukhamedov, Farrukh, Saburov, Mansoor, Khakimov, Otabek
• Format: Article
• Language: English; English; English
• Published: Maik Nauka Publishing / Springer SBM 2016
• Subjects: Q Science (General)
• Online Access: http://irep.iium.edu.my/58349/1/58349_Translation-invariant%20p-adic%20quasi.pdf; http://irep.iium.edu.my/58349/2/58349_Translation-invariant%20p-adic%20quasi_SCOPUS.pdf; http://irep.iium.edu.my/58349/3/58349_Translation-invariant%20p-adic%20quasi_WOS.pdf; http://irep.iium.edu.my/58349/; https://link.springer.com/article/10.1134/S0040577916040127

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. © 2016, Pleiades Publishing, Ltd.