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Two-dimensional Ising model with non-homogenous interactions

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.

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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

Item Type: Conference or Workshop Item (Plenary Papers)
Additional Information: 4430/52990
Uncontrolled Keywords: Ising model, non-homogenous interactions
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: Prof. Nasir Ganikhodjaev
Date Deposited: 06 Dec 2016 11:32
Last Modified: 17 Aug 2019 19:20
URI: http://irep.iium.edu.my/id/eprint/52990

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