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

Rukiah Bin Ali, Farrukh Mukhamedov, Chin Hee Pah

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1 Citation (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 languageEnglish
Article number012032
JournalJournal of Physics: Conference Series
Volume435
Issue number1
DOIs
Publication statusPublished - 2013
Externally publishedYes
Event4th International Conference on the Advancement of Science and Technology 2012: Contemporary Mathematics, Mathematical Physics and Their Applications, iCAST 2012 - Kuantan, Malaysia
Duration: Nov 7 2012Nov 10 2012

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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