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

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 prese...

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Main Authors:	Mukhamedov, Farrukh, Souissi, Abdessatar, Barhoumi, Abdessatar
Format:	Article
Language:	English English English
Published:	Springer Netherlands 2016
Subjects:	QA Mathematics QC Physics
Online Access:	http://irep.iium.edu.my/53490/ http://irep.iium.edu.my/53490/ http://irep.iium.edu.my/53490/ http://irep.iium.edu.my/53490/1/53490_On%20an%20Algebraic%20Propert.pdf http://irep.iium.edu.my/53490/2/53490_On%20an%20Algebraic%20Propert_WOS.pdf http://irep.iium.edu.my/53490/3/53490_On%20an%20Algebraic%20Propert_SCOPUS.pdf

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spelling	iium-534902017-10-21T07:33:58Z http://irep.iium.edu.my/53490/ On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree Mukhamedov, Farrukh Souissi, Abdessatar Barhoumi, Abdessatar QA Mathematics QC Physics 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 Springer Netherlands 2016-12 Article PeerReviewed application/pdf en http://irep.iium.edu.my/53490/1/53490_On%20an%20Algebraic%20Propert.pdf application/pdf en http://irep.iium.edu.my/53490/2/53490_On%20an%20Algebraic%20Propert_WOS.pdf application/pdf en http://irep.iium.edu.my/53490/3/53490_On%20an%20Algebraic%20Propert_SCOPUS.pdf 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 https://link.springer.com/article/10.1007/s11040-016-9225-x 10.1007/s11040-016-9225-x
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English English
topic	QA Mathematics QC Physics
spellingShingle	QA Mathematics QC Physics Mukhamedov, Farrukh Souissi, Abdessatar Barhoumi, Abdessatar On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree
description	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
format	Article
author	Mukhamedov, Farrukh Souissi, Abdessatar Barhoumi, Abdessatar
author_facet	Mukhamedov, Farrukh Souissi, Abdessatar Barhoumi, Abdessatar
author_sort	Mukhamedov, Farrukh
title	On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree
title_short	On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree
title_full	On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree
title_fullStr	On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree
title_full_unstemmed	On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree
title_sort	on an algebraic property of the disordered phase of the ising model with competing interactions on a cayley tree
publisher	Springer Netherlands
publishDate	2016
url	http://irep.iium.edu.my/53490/ http://irep.iium.edu.my/53490/ http://irep.iium.edu.my/53490/ http://irep.iium.edu.my/53490/1/53490_On%20an%20Algebraic%20Propert.pdf http://irep.iium.edu.my/53490/2/53490_On%20an%20Algebraic%20Propert_WOS.pdf http://irep.iium.edu.my/53490/3/53490_On%20an%20Algebraic%20Propert_SCOPUS.pdf
first_indexed	2023-09-18T21:15:40Z
last_indexed	2023-09-18T21:15:40Z
_version_	1777411544900960256

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

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