Phase diagram and phase transitions of the Potts model with external magnetic field
The physical phenomenon of phase transition is reflected in mathematical model by non-uniqueness of the Gibbs measures and phase diagram of the model describes a morphology of phases, stability of phases, different transitions from one phase to another and corresponding transition lines. We study th...
| Main Authors: | , , |
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| Format: | Proceeding Paper |
| Language: | English |
| Published: |
2009
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/13709/ http://irep.iium.edu.my/13709/1/P199.pdf |
| _version_ | 1848777596328738816 |
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| author | Ganikhodjaev, Nasir Nawi, Ashraf Mohamed Rodzhan, Mohd Hirzie |
| author_facet | Ganikhodjaev, Nasir Nawi, Ashraf Mohamed Rodzhan, Mohd Hirzie |
| author_sort | Ganikhodjaev, Nasir |
| building | IIUM Repository |
| collection | Online Access |
| description | The physical phenomenon of phase transition is reflected in mathematical model by non-uniqueness of the Gibbs measures and phase diagram of the model describes a morphology of phases, stability of phases, different transitions from one phase to another and corresponding transition lines. We study the phase diagram for the Potts model on a Cayley tree with nearest-neighbor interaction J in the presence of an external magnetic field h. To perform this study,an iterative scheme similar to that appearing in real space renormalization group frameworks is established. The phase diagram is fully determined in the T/J −h/J space for all values and signs of J and h. This phase diagram explicitly demonstrates relations between parameters J, h and T, where as in previous works of Peruggi et al such relations were implicit. |
| first_indexed | 2025-11-14T14:48:30Z |
| format | Proceeding Paper |
| id | iium-13709 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:48:30Z |
| publishDate | 2009 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-137092012-02-01T11:44:47Z http://irep.iium.edu.my/13709/ Phase diagram and phase transitions of the Potts model with external magnetic field Ganikhodjaev, Nasir Nawi, Ashraf Mohamed Rodzhan, Mohd Hirzie QA Mathematics The physical phenomenon of phase transition is reflected in mathematical model by non-uniqueness of the Gibbs measures and phase diagram of the model describes a morphology of phases, stability of phases, different transitions from one phase to another and corresponding transition lines. We study the phase diagram for the Potts model on a Cayley tree with nearest-neighbor interaction J in the presence of an external magnetic field h. To perform this study,an iterative scheme similar to that appearing in real space renormalization group frameworks is established. The phase diagram is fully determined in the T/J −h/J space for all values and signs of J and h. This phase diagram explicitly demonstrates relations between parameters J, h and T, where as in previous works of Peruggi et al such relations were implicit. 2009-06 Proceeding Paper NonPeerReviewed application/pdf en http://irep.iium.edu.my/13709/1/P199.pdf Ganikhodjaev, Nasir and Nawi, Ashraf Mohamed and Rodzhan, Mohd Hirzie (2009) Phase diagram and phase transitions of the Potts model with external magnetic field. In: 5th Asian Mathematical Conference, Malaysia 2009, 22 - 26 June 2009, Kuala Lumpur. (Unpublished) |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Nawi, Ashraf Mohamed Rodzhan, Mohd Hirzie Phase diagram and phase transitions of the Potts model with external magnetic field |
| title | Phase diagram and phase transitions of the Potts model with external magnetic field |
| title_full | Phase diagram and phase transitions of the Potts model with external magnetic field |
| title_fullStr | Phase diagram and phase transitions of the Potts model with external magnetic field |
| title_full_unstemmed | Phase diagram and phase transitions of the Potts model with external magnetic field |
| title_short | Phase diagram and phase transitions of the Potts model with external magnetic field |
| title_sort | phase diagram and phase transitions of the potts model with external magnetic field |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/13709/ http://irep.iium.edu.my/13709/1/P199.pdf |