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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...

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Main Authors: Ali, Rukiah, Mukhamedov, Farrukh, Pah, Chin Hee
Format: Article
Language:English
Published: Institute of Physics Publishing (UK) 2013
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/30083/1/mfrapch-JPCS%282013%29.pdf
http://irep.iium.edu.my/30083/
http://dx.doi.org/10.1088/1742-6596/435/1/012032
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spelling my.iium.irep.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 REM 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
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Ali, Rukiah
Mukhamedov, Farrukh
Pah, Chin Hee
Ising model with competing interactions on Cayley tree of Order 4: an analytic solution
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.
format Article
author Ali, Rukiah
Mukhamedov, Farrukh
Pah, Chin Hee
author_facet Ali, Rukiah
Mukhamedov, Farrukh
Pah, Chin Hee
author_sort Ali, Rukiah
title 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_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_sort ising model with competing interactions on cayley tree of order 4: an analytic solution
publisher Institute of Physics Publishing (UK)
publishDate 2013
url http://irep.iium.edu.my/30083/1/mfrapch-JPCS%282013%29.pdf
http://irep.iium.edu.my/30083/
http://dx.doi.org/10.1088/1742-6596/435/1/012032
_version_ 1643609815727996928
score 13.149126

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