Ising model with competing interactions on Cayley tree of Order 4: an analytic solution
We investigate an Ising model with two restricted competing interactions (nearest neighbors, and one-level neighbors) on the Cayley tree of order four. We derive a recurrent equation for the Cayley tree of order k. We found an analytic solution for the given interactions in the case of order 4. Our...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Institute of Physics Publishing (UK)
2013
|
| Subjects: | |
| Online Access: | http://irep.iium.edu.my/30083/1/mfrapch-JPCS%282013%29.pdf |
| _version_ | 1796878008352505856 |
|---|---|
| author | Ali, Rukiah Mukhamedov, Farrukh Pah, Chin Hee |
| author_facet | Ali, Rukiah Mukhamedov, Farrukh Pah, Chin Hee |
| author_sort | Ali, Rukiah |
| collection | IIUM |
| description | We investigate an Ising model with two restricted competing interactions (nearest neighbors, and one-level neighbors) on the Cayley tree of order four. We derive a recurrent equation for the Cayley tree of order k. We found an analytic solution for the given interactions in the case of order 4. Our result of the critical curve shows the existence of the phase transition occurs in this model. We also give the calculation of the free energy from the description of Gibbs measure of the given Hamiltonian on Cayley tree of order four. |
| first_indexed | 2024-03-05T23:15:27Z |
| format | Article |
| id | oai:generic.eprints.org:30083 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-05T23:15:27Z |
| publishDate | 2013 |
| publisher | Institute of Physics Publishing (UK) |
| record_format | dspace |
| spelling | oai:generic.eprints.org:300832013-07-24T04:48:57Z http://irep.iium.edu.my/30083/ Ising model with competing interactions on Cayley tree of Order 4: an analytic solution Ali, Rukiah Mukhamedov, Farrukh Pah, Chin Hee QA Mathematics We investigate an Ising model with two restricted competing interactions (nearest neighbors, and one-level neighbors) on the Cayley tree of order four. We derive a recurrent equation for the Cayley tree of order k. We found an analytic solution for the given interactions in the case of order 4. Our result of the critical curve shows the existence of the phase transition occurs in this model. We also give the calculation of the free energy from the description of Gibbs measure of the given Hamiltonian on Cayley tree of order four. Institute of Physics Publishing (UK) 2013 Article PeerReviewed application/pdf en http://irep.iium.edu.my/30083/1/mfrapch-JPCS%282013%29.pdf Ali, Rukiah and Mukhamedov, Farrukh and Pah, Chin Hee (2013) Ising model with competing interactions on Cayley tree of Order 4: an analytic solution. Journal of Physics: Conference Series, 435. 012032. ISSN 1742-6588 (P), 1742-6596 (O) http://dx.doi.org/10.1088/1742-6596/435/1/012032 doi:10.1088/1742-6596/435/1/012032 |
| spellingShingle | QA Mathematics Ali, Rukiah Mukhamedov, Farrukh Pah, Chin Hee Ising model with competing interactions on Cayley tree of Order 4: an analytic solution |
| title | Ising model with competing interactions on Cayley tree of Order 4: an analytic solution |
| title_full | Ising model with competing interactions on Cayley tree of Order 4: an analytic solution |
| title_fullStr | Ising model with competing interactions on Cayley tree of Order 4: an analytic solution |
| title_full_unstemmed | Ising model with competing interactions on Cayley tree of Order 4: an analytic solution |
| title_short | Ising model with competing interactions on Cayley tree of Order 4: an analytic solution |
| title_sort | ising model with competing interactions on cayley tree of order 4 an analytic solution |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/30083/1/mfrapch-JPCS%282013%29.pdf |
| work_keys_str_mv | AT alirukiah isingmodelwithcompetinginteractionsoncayleytreeoforder4ananalyticsolution AT mukhamedovfarrukh isingmodelwithcompetinginteractionsoncayleytreeoforder4ananalyticsolution AT pahchinhee isingmodelwithcompetinginteractionsoncayleytreeoforder4ananalyticsolution |