Behaviors of Phase Diagrams of Ising Model with Competing Ternary and Binary Interactions on a Cayley Tree of Arbitrary Order

• Authors: H. Akin , N. Ganikhodjaev , S. Uguz , S. Temir
• Languages of publication: EN

Abstracts

EN

An Ising model with competing interactions has recently been studied extensively because of the appearance of nontrivial magnetic orderings. In this paper, we study the phase diagrams for the Ising model on a Cayley tree with competing nearest-neighbor interactions J and ternary prolonged interactions J_{t_{p}} on a Cayley tree of arbitrary order k and compare with the phase diagrams obtained in Uguz et al. and Vannimenus results for the Ising model on a Cayley tree with competing nearest-neighbor interactions J and ternary prolonged interactions J_{p}. For some values of k, we obtain phase diagrams of the model. We clarify the role of order k of the Cayley tree. We also plot the variation of the wave vector with temperature.

Keywords

EN

05.50.+q; 64.60.-i; 64.60.De

Discipline

• 64.60.De: Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.)
• 64.60.-i: General studies of phase transitions(see also 63.70.+h Statistical mechanics of lattice vibrations and displacive phase transitions; for critical phenomena in solid surfaces and interfaces, and in magnetism, see 68.35.Rh, and 75.40.-s, respectively)
• 05.50.+q: Lattice theory and statistics (Ising, Potts, etc.)(see also 64.60.Cn Order-disorder transformations, and 75.10.Hk Classical spin models)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 1
• Pages: 104-107

Dates

published

2012-01

Contributors

author

H. Akin

• Faculty of Education, Department of Mathematics, Zirve University, Gaziantep, 27260, Turkey

author

N. Ganikhodjaev

• Department of Computational and Theoretical Sciences, Faculty of Science, IIUM, 25200 Kuantan, Malaysia

author

S. Uguz

• Arts and Science Faculty, Department of Mathematics, Harran University, Sanliurfa, 63120, Turkey

author

S. Temir

• Arts and Science Faculty, Department of Mathematics, Harran University, Sanliurfa, 63120, Turkey

References

• 1. S. Uguz, N.N. Ganikhodjaev, S. Temir, H. Akın, H., AIP Conf. Proc. 1281, 2074 (2010)
• 2. J. Vannimenus, Z. Phys. B 43, 141 (1981)
• 3. S. Katsura, M. Takizawa, Prog. Theor. Phys. 51, 82 (1974)
• 4. S. Uguz, H. Akin, Physica A 389, 1839 (2010)
• 5. S. Inawashiro, C.J. Thompson, Phys. Lett. 97A, 245 (1983)
• 6. M. Mariz, C. Tsalis, A.L. Albuquerque, J. Statist. Phys. 40, 577 (1985)
• 7. S. Uguz, H. Akin, Chinese J. Phys. 49, 785 (2011)
• 8. N.N. Ganikhodjaev, H. Akin, S. Uguz, S. Temir, Phase Transitions: A Multinational Journal 84, 1045 (2011)
• 9. K. Fesser, H.J. Herrmann, J. Phys. A 17, 1493 (1984)

Identifiers

DOI

10.12693/APhysPolA.121.104