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

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 qu...

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Bibliographic Details
Published in:	Theoretical and mathematical physics Vol. 187; no. 1; pp. 583 - 602
Main Authors:	Mukhamedov, F. M., Saburov, M. Kh, Khakimov, O. Kh
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-04-2016
Subjects:	Applications of Mathematics Mathematical and Computational Physics Physics Physics and Astronomy Theoretical adic Gibbs measure phase transition adic numbers Cayley tree Ising–Vannimenus model dynamical system
Online Access:	Get full text
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Summary:	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 .
ISSN:	0040-5779 1573-9333
DOI:	10.1134/S0040577916040127