Two-dimensional Ising model with non-homogenous interactions

In this paper we investigate the Ising model on Z2 with competing interactions. In this model we consider J1 as horizontal interactions and J2 as vertical interactions where J1,J2 > 0. We prove that this model can reach a phase transition. Onsager considered the case where horizontal interaction...

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Main Authors:	Ganikhodjaev, Nasir, Ibrahim, Huda Husna
Format:	Conference or Workshop Item
Language:	English English English
Published:	American Institute of Physics 2017
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/52990/ http://irep.iium.edu.my/52990/ http://irep.iium.edu.my/52990/ http://irep.iium.edu.my/52990/54/52990%20Two-dimensional%20Ising%20Model.pdf http://irep.iium.edu.my/52990/48/52990_Two-dimensional%20Ising%20model%20with_Scopus.pdf http://irep.iium.edu.my/52990/60/52990_Two-dimensional%20Ising%20model%20_wos.pdf

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recordtype	eprints
spelling	iium-529902019-08-17T11:20:27Z http://irep.iium.edu.my/52990/ Two-dimensional Ising model with non-homogenous interactions Ganikhodjaev, Nasir Ibrahim, Huda Husna QA Mathematics In this paper we investigate the Ising model on Z2 with competing interactions. In this model we consider J1 as horizontal interactions and J2 as vertical interactions where J1,J2 > 0. We prove that this model can reach a phase transition. Onsager considered the case where horizontal interaction parameter J1 and vertical interaction parameter J2 are different. For any fixed J1 and J2, he showed that below a critical temperature Tc which depends on J1 and J2, phase transition occurs using some matrix transfer method. However in this paper we will prove the existence of phase transition using contours methods introduced by Sinai. We will show that there exists a β0 > 0 such that for β > β0 there exist at least two limit Gibbs distribution which leads to the phenomena of phase transition American Institute of Physics 2017-04-27 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/52990/54/52990%20Two-dimensional%20Ising%20Model.pdf application/pdf en http://irep.iium.edu.my/52990/48/52990_Two-dimensional%20Ising%20model%20with_Scopus.pdf application/pdf en http://irep.iium.edu.my/52990/60/52990_Two-dimensional%20Ising%20model%20_wos.pdf Ganikhodjaev, Nasir and Ibrahim, Huda Husna (2017) Two-dimensional Ising model with non-homogenous interactions. In: The 4th International Conference On Mathematical Sciences (ICMS4), 15th-17th November 2016, Putrajaya. https://aip.scitation.org/doi/abs/10.1063/1.4980984 10.1063/1.4980984
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
spellingShingle	QA Mathematics Ganikhodjaev, Nasir Ibrahim, Huda Husna Two-dimensional Ising model with non-homogenous interactions
description	In this paper we investigate the Ising model on Z2 with competing interactions. In this model we consider J1 as horizontal interactions and J2 as vertical interactions where J1,J2 > 0. We prove that this model can reach a phase transition. Onsager considered the case where horizontal interaction parameter J1 and vertical interaction parameter J2 are different. For any fixed J1 and J2, he showed that below a critical temperature Tc which depends on J1 and J2, phase transition occurs using some matrix transfer method. However in this paper we will prove the existence of phase transition using contours methods introduced by Sinai. We will show that there exists a β0 > 0 such that for β > β0 there exist at least two limit Gibbs distribution which leads to the phenomena of phase transition
format	Conference or Workshop Item
author	Ganikhodjaev, Nasir Ibrahim, Huda Husna
author_facet	Ganikhodjaev, Nasir Ibrahim, Huda Husna
author_sort	Ganikhodjaev, Nasir
title	Two-dimensional Ising model with non-homogenous interactions
title_short	Two-dimensional Ising model with non-homogenous interactions
title_full	Two-dimensional Ising model with non-homogenous interactions
title_fullStr	Two-dimensional Ising model with non-homogenous interactions
title_full_unstemmed	Two-dimensional Ising model with non-homogenous interactions
title_sort	two-dimensional ising model with non-homogenous interactions
publisher	American Institute of Physics
publishDate	2017
url	http://irep.iium.edu.my/52990/ http://irep.iium.edu.my/52990/ http://irep.iium.edu.my/52990/ http://irep.iium.edu.my/52990/54/52990%20Two-dimensional%20Ising%20Model.pdf http://irep.iium.edu.my/52990/48/52990_Two-dimensional%20Ising%20model%20with_Scopus.pdf http://irep.iium.edu.my/52990/60/52990_Two-dimensional%20Ising%20model%20_wos.pdf
first_indexed	2023-09-18T21:15:02Z
last_indexed	2023-09-18T21:15:02Z
_version_	1777411505257447424

Two-dimensional Ising model with non-homogenous interactions

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