On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree

Mukhamedov, Farrukh and Souissi, Abdessatar and Barhoumi, Abdessatar (2016) On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree. Mathematical Physics Analysis and Geometry, 19 (4). 21-1 -21-18. ISSN 1385-0172 E-ISSN 1572-9656

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Abstract

It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the present paper, we first aiming to analyze the correspondence between Gibbs measures and QMC’s on trees. Namely, we establish that states associated with translation invariant Gibbs measures of the model can be seen as diagonal quantum Markov chains on some quasi local algebra. Then as an application of the established correspondence, we study some algebraic property of the disordered phase of the Ising model with competing interactions on the Cayley tree of order two. More exactly, we prove that a state corresponding to the disordered phase is not quasi-equivalent to other states associated with translation invariant Gibbs measures. This result shows how the translation invariant states relate to each other, which is even a new phenomena in the classical setting. To establish the main result we basically employ methods of quantum Markov chains

Item Type:	Article (Journal)
Additional Information:	5537/53490
Uncontrolled Keywords:	Cayley tree; Competing interaction; Disordered phase; Ising type model; Quantum Markov chain; Quasi-equivalence
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	14 Apr 2017 17:43
Last Modified:	21 Oct 2017 15:33
URI:	http://irep.iium.edu.my/id/eprint/53490

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