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

Mukhamedov, Farrukh and Saburov, Mansoor and Khakimov, Otabek (2016) Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree. Theoretical and Mathematical Physics(Russian Federation), 187 (1). pp. 583-602. ISSN 0040-5779 E-ISSN 1573-9333

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	5537/58349
Uncontrolled Keywords:	p-adic numbers, Ising–Vannimenus model, p-adic Gibbs measure, dynamical system, phase transition, Cayley tree
Subjects:	Q Science > Q Science (General)
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	05 Oct 2017 16:49
Last Modified:	05 Oct 2017 16:49
URI:	http://irep.iium.edu.my/id/eprint/58349

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