Phase transitions for lattice models on Cayley trees /
In this research, we investigate phase transitions phenomenon for two lattice models, i.e., Ising model and λ-model on Cayley trees. For the first result, we prove the existence of phase transitions by analyzing the recurrent equation that derived from the Ising model with competing interactions (ne...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
Kuantan, Pahang :
Kulliyyah of Science, International Islamic University Malaysia,
2017
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| Subjects: | |
| Online Access: | Click here to view 1st 24 pages of the thesis. Members can view fulltext at the specified PCs in the library. |
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| 100 | 0 | |a Mohd Hakim bin Jamil, |e author | |
| 245 | 1 | 0 | |a Phase transitions for lattice models on Cayley trees / |c by Mohd Hakim bin Jamil |
| 264 | 1 | |a Kuantan, Pahang : |b Kulliyyah of Science, International Islamic University Malaysia, |c 2017 | |
| 300 | |a x, 53 leaves : |b illustrations ; |c 30cm. | ||
| 336 | |2 rdacontent |a text | ||
| 347 | |2 rdaft |a text file |b PDF | ||
| 502 | |a Thesis (MSCTS)--International Islamic University Malaysia, 2017. | ||
| 504 | |a Includes bibliographical references (leaves 50-52). | ||
| 520 | |a In this research, we investigate phase transitions phenomenon for two lattice models, i.e., Ising model and λ-model on Cayley trees. For the first result, we prove the existence of phase transitions by analyzing the recurrent equation that derived from the Ising model with competing interactions (nearest neighbors, and one-level neighbors) on the Cayley tree of order five. We found an exact solution for the given interactions in the case of order 5. We confirm a special case of the conjecture for the critical curve that separate the region of single fixed point and multiple fixed points that have been proposed by Pah and Ali (2013). For the second result, we study the λ-model with spin values {1, 2, 3} on the Cayley tree of order two. We calculated the ground states energy of the λ-model. We proved that for some cases for the ground states, there exist three translation-invariant, periodic and uncountable number of ground states. Further, we described all translation-invariant Gibb measures for λ-model. Lastly, we proved the existence of 2-periodic Gibbs measures for λ-model by considering some special cases. | ||
| 596 | |a 1 6 | ||
| 655 | 7 | |a Theses, IIUM local | |
| 690 | |a Dissertations, Academic |x Department of Computational and Theoretical Sciences |z IIUM | ||
| 710 | 2 | |a International Islamic University Malaysia. |b Department of Computational and Theoritical Sciences | |
| 856 | 4 | |u https://lib.iium.edu.my/mom/services/mom/document/getFile/iuwmqVfTtgbi0Mm2UMmUCMI7dguQbIWU20180518094353269 |z Click here to view 1st 24 pages of the thesis. Members can view fulltext at the specified PCs in the library. | |
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