On Gibbs Measures of the Potts Model with Three Competing Interactions on Cayley Tree of Order 3

• Authors: H. Akin , H. Saygılı
• Languages of publication: EN

Abstracts

EN

In this paper, we consider the Potts model with competing interactions on the Cayley tree of order three. We give the Potts model on the Cayley tree and its recursion relation. We construct the Gibbs states corresponding to the model by using Markov random field method. We calculate the critical curve, such that there is a phase transition for the model. We show that there are phase transition of the model for some given parameters. We extend the results obtained by Akin and Temir (Condensed Matt. Phys. 14, 23003 (2011)).

Keywords

EN

05.50.+q; 64.60.-i; 75.10.Hk; 64.60.De

Discipline

• 75.10.Hk: Classical spin models
• 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: 2016
• Volume: 129
• Issue: 4
• Pages: 845-848

Dates

published

2016-04

Contributors

author

H. Akin

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

author

H. Saygılı

• Gaziantep University, Science and Art Faculty, Department of Mathematics, Gaziantep, 27260, Turkey

References

• [1] F.Y. Wu, Rev. Mod. Phys. 54, 235 (1982), doi: 10.1103/RevModPhys.54.235
• [2] H. Akın, S. Temir, Cond. Matt. Phys. 14, 23003 (2011), doi: 10.5488/CMP.14.23003
• [3] U.A. Rozikov, H. Akın, S. Uguz, Math. Phys. Anal. Geom. 17, 103 (2014), doi: 10.1007/s11040-014-9144-7
• [4] H. Akın, U.A. Rozikov, S. Temir, J. Stat. Phys. 142, 314 (2011), doi: 10.1007/s10955-010-0106-6
• [5] H. Akın, N. Ganikhodjaev, S. Temir, S. Uguz, Acta Phys. Pol. A 123, 484 (2013), doi: 10.12693/APhysPolA.123.484
• [6] N. Ganikhodjaev, H. Akın, S. Uguz, S. Temir, J. Stat. Mech.-Theory Exp. 2011, P03025 (2011), doi: 10.1088/1742-5468/2011/03/P03025
• [7] H.O. Georgii, Gibbs measures and phase transitions, De Gruyter studies in Mathematics Vol. 9, Berlin 1988

Identifiers

DOI

10.12693/APhysPolA.129.845