Ising model with competing interactions on cayley tree of order 4: An analytic solution

Rukiah Bin Ali; Farrukh Mukhamedov; Chin Hee Pah

doi:10.1088/1742-6596/435/1/012032

Ising model with competing interactions on cayley tree of order 4: An analytic solution

Rukiah Bin Ali, Farrukh Mukhamedov, Chin Hee Pah

Research output: Contribution to journal › Conference article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Article number	012032
Journal	Journal of Physics: Conference Series
Volume	435
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/435/1/012032
Publication status	Published - 2013
Externally published	Yes
Event	4th International Conference on the Advancement of Science and Technology 2012: Contemporary Mathematics, Mathematical Physics and Their Applications, iCAST 2012 - Kuantan, Malaysia Duration: Nov 7 2012 → Nov 10 2012

ASJC Scopus subject areas

Physics and Astronomy(all)

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title = "Ising model with competing interactions on cayley tree of order 4: An analytic solution",

abstract = "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.",

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T1 - Ising model with competing interactions on cayley tree of order 4

T2 - 4th International Conference on the Advancement of Science and Technology 2012: Contemporary Mathematics, Mathematical Physics and Their Applications, iCAST 2012

AU - Ali, Rukiah Bin

AU - Mukhamedov, Farrukh

AU - Pah, Chin Hee

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

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DO - 10.1088/1742-6596/435/1/012032

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AN - SCOPUS:84878042010

SN - 1742-6588

VL - 435

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012032

Y2 - 7 November 2012 through 10 November 2012

ER -

Ising model with competing interactions on cayley tree of order 4: An analytic solution

Abstract

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