Zeros of the 3-state Potts model partition function for the square lattice revisited

We compute the exact partition function for the 3-state Potts model on square lattices of several sizes larger than previously accessible. Making comparison with the exactly solved Ising model we show that, for aspects of the analytic structure close to the ferromagnetic transition point, these latt...

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Main Authors:	Martin, Paul Purdon, Zakaria, Siti Fatimah
Format:	Article
Language:	English English
Published:	IOP Publishing 2019
Subjects:	QA Mathematics QC Physics
Online Access:	http://irep.iium.edu.my/74165/ http://irep.iium.edu.my/74165/ http://irep.iium.edu.my/74165/ http://irep.iium.edu.my/74165/1/JSTAT_037P_0119%281%29.pdf http://irep.iium.edu.my/74165/7/74165_Zeros%20of%20the%203-state%20Potts%20model%20partition%20function%20for%20the%20square%20lattice%20revisited_Scopus.pdf

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recordtype	eprints
spelling	iium-741652019-11-21T07:04:41Z http://irep.iium.edu.my/74165/ Zeros of the 3-state Potts model partition function for the square lattice revisited Martin, Paul Purdon Zakaria, Siti Fatimah QA Mathematics QC Physics We compute the exact partition function for the 3-state Potts model on square lattices of several sizes larger than previously accessible. Making comparison with the exactly solved Ising model we show that, for aspects of the analytic structure close to the ferromagnetic transition point, these lattices are large enough to approach the thermodynamic limit. Subject to certain assumptions this allows for computation of estimates for the specific heat critical exponent. We thus obtain an estimate for this exponent. The estimate is consistent with the known result, thus demonstrating the potential use of this method for other models. We also discuss the antiferromagnetic transition. IOP Publishing 2019-08 Article PeerReviewed application/pdf en http://irep.iium.edu.my/74165/1/JSTAT_037P_0119%281%29.pdf application/pdf en http://irep.iium.edu.my/74165/7/74165_Zeros%20of%20the%203-state%20Potts%20model%20partition%20function%20for%20the%20square%20lattice%20revisited_Scopus.pdf Martin, Paul Purdon and Zakaria, Siti Fatimah (2019) Zeros of the 3-state Potts model partition function for the square lattice revisited. Journal of Statistical Mechanics: Theory and Experiment, 2019. pp. 2-25. E-ISSN 1742-5468 https://iopscience.iop.org/article/10.1088/1742-5468/ab2905 10.1088/1742-5468/ab2905
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English
topic	QA Mathematics QC Physics
spellingShingle	QA Mathematics QC Physics Martin, Paul Purdon Zakaria, Siti Fatimah Zeros of the 3-state Potts model partition function for the square lattice revisited
description	We compute the exact partition function for the 3-state Potts model on square lattices of several sizes larger than previously accessible. Making comparison with the exactly solved Ising model we show that, for aspects of the analytic structure close to the ferromagnetic transition point, these lattices are large enough to approach the thermodynamic limit. Subject to certain assumptions this allows for computation of estimates for the specific heat critical exponent. We thus obtain an estimate for this exponent. The estimate is consistent with the known result, thus demonstrating the potential use of this method for other models. We also discuss the antiferromagnetic transition.
format	Article
author	Martin, Paul Purdon Zakaria, Siti Fatimah
author_facet	Martin, Paul Purdon Zakaria, Siti Fatimah
author_sort	Martin, Paul Purdon
title	Zeros of the 3-state Potts model partition function for the square lattice revisited
title_short	Zeros of the 3-state Potts model partition function for the square lattice revisited
title_full	Zeros of the 3-state Potts model partition function for the square lattice revisited
title_fullStr	Zeros of the 3-state Potts model partition function for the square lattice revisited
title_full_unstemmed	Zeros of the 3-state Potts model partition function for the square lattice revisited
title_sort	zeros of the 3-state potts model partition function for the square lattice revisited
publisher	IOP Publishing
publishDate	2019
url	http://irep.iium.edu.my/74165/ http://irep.iium.edu.my/74165/ http://irep.iium.edu.my/74165/ http://irep.iium.edu.my/74165/1/JSTAT_037P_0119%281%29.pdf http://irep.iium.edu.my/74165/7/74165_Zeros%20of%20the%203-state%20Potts%20model%20partition%20function%20for%20the%20square%20lattice%20revisited_Scopus.pdf
first_indexed	2023-09-18T21:45:04Z
last_indexed	2023-09-18T21:45:04Z
_version_	1777413395304153088

Zeros of the 3-state Potts model partition function for the square lattice revisited

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