The zeros distribution of Z_5-symmetric model on a triangular lattice
We study the -symmetric model with the nearest neighbour interaction between molecular dipole of five spin directions i.e. Q=5 which called as the -symmetric model on a triangular lattice. We investigate the zeros of partition function and the relationship to the phase transition. Initially, the mod...
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2020
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| Online Access: | http://irep.iium.edu.my/80923/ http://irep.iium.edu.my/80923/1/80923_The%20zeros%20distribution%20of%20Z_5-symmetric.pdf http://irep.iium.edu.my/80923/7/80923_The%20zeros%20distribution%20of%20Z%285%29-symmetric%20model_wos.pdf |
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| author | Zakaria, Siti Fatimah Mohd Manshur, Nor Sakinah |
| author_facet | Zakaria, Siti Fatimah Mohd Manshur, Nor Sakinah |
| author_sort | Zakaria, Siti Fatimah |
| building | IIUM Repository |
| collection | Online Access |
| description | We study the -symmetric model with the nearest neighbour interaction between molecular dipole of five spin directions i.e. Q=5 which called as the -symmetric model on a triangular lattice. We investigate the zeros of partition function and the relationship to the phase transition. Initially, the model is defined on a triangular lattice graph with the nearest neighbour interaction. The partition function is then computed using a transfer matrix approach. We analyse the system by computing the zeros of the polynomial partition function using the Newton-Raphson method and then plot the zeros in a complex plane. For this lattice, the result shows that for specific type of energy level there are multiple line curves approaching real axis in the complex plane. The equation of the specific heat is produced and then plotted for comparison. Motivated from the work by Martin (1991) on models on square lattice, we extend the previous study to different lattice type that is triangular lattice. |
| first_indexed | 2025-11-14T17:50:29Z |
| format | Article |
| id | iium-80923 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T17:50:29Z |
| publishDate | 2020 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-809232021-01-21T01:07:31Z http://irep.iium.edu.my/80923/ The zeros distribution of Z_5-symmetric model on a triangular lattice Zakaria, Siti Fatimah Mohd Manshur, Nor Sakinah QA Mathematics QC Physics We study the -symmetric model with the nearest neighbour interaction between molecular dipole of five spin directions i.e. Q=5 which called as the -symmetric model on a triangular lattice. We investigate the zeros of partition function and the relationship to the phase transition. Initially, the model is defined on a triangular lattice graph with the nearest neighbour interaction. The partition function is then computed using a transfer matrix approach. We analyse the system by computing the zeros of the polynomial partition function using the Newton-Raphson method and then plot the zeros in a complex plane. For this lattice, the result shows that for specific type of energy level there are multiple line curves approaching real axis in the complex plane. The equation of the specific heat is produced and then plotted for comparison. Motivated from the work by Martin (1991) on models on square lattice, we extend the previous study to different lattice type that is triangular lattice. 2020-06-15 Article PeerReviewed application/pdf en http://irep.iium.edu.my/80923/1/80923_The%20zeros%20distribution%20of%20Z_5-symmetric.pdf application/pdf en http://irep.iium.edu.my/80923/7/80923_The%20zeros%20distribution%20of%20Z%285%29-symmetric%20model_wos.pdf Zakaria, Siti Fatimah and Mohd Manshur, Nor Sakinah (2020) The zeros distribution of Z_5-symmetric model on a triangular lattice. Malaysian Journal of Fundamental and Applied Sciences, 16(2020) (3). pp. 307-313. ISSN 2289 5981 E-ISSN 2289 599x |
| spellingShingle | QA Mathematics QC Physics Zakaria, Siti Fatimah Mohd Manshur, Nor Sakinah The zeros distribution of Z_5-symmetric model on a triangular lattice |
| title | The zeros distribution of Z_5-symmetric model on a triangular lattice |
| title_full | The zeros distribution of Z_5-symmetric model on a triangular lattice |
| title_fullStr | The zeros distribution of Z_5-symmetric model on a triangular lattice |
| title_full_unstemmed | The zeros distribution of Z_5-symmetric model on a triangular lattice |
| title_short | The zeros distribution of Z_5-symmetric model on a triangular lattice |
| title_sort | zeros distribution of z_5-symmetric model on a triangular lattice |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/80923/ http://irep.iium.edu.my/80923/1/80923_The%20zeros%20distribution%20of%20Z_5-symmetric.pdf http://irep.iium.edu.my/80923/7/80923_The%20zeros%20distribution%20of%20Z%285%29-symmetric%20model_wos.pdf |