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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| Format: | Article |
| Language: | English English English |
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IOP Publishing
2019
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| Online Access: | 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 http://irep.iium.edu.my/74165/13/74165_Zeros%20of%20the%203-state%20Potts%20model%20partition%20function_wos.pdf |
| _version_ | 1848787921196285952 |
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| author | Martin, Paul Purdon Zakaria, Siti Fatimah |
| author_facet | Martin, Paul Purdon Zakaria, Siti Fatimah |
| author_sort | Martin, Paul Purdon |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T17:32:36Z |
| format | Article |
| id | iium-74165 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English English |
| last_indexed | 2025-11-14T17:32:36Z |
| publishDate | 2019 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-741652020-04-05T21:49:19Z 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 application/pdf en http://irep.iium.edu.my/74165/13/74165_Zeros%20of%20the%203-state%20Potts%20model%20partition%20function_wos.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 |
| 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 |
| title | 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_short | 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 |
| topic | QA Mathematics QC Physics |
| 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 http://irep.iium.edu.my/74165/13/74165_Zeros%20of%20the%203-state%20Potts%20model%20partition%20function_wos.pdf |