Description of Extreme Gibbs Measures for the Ising Model with Three Interactions

H. Akina, N. Ganikhodjaevb, S. Temirc and S. Uguzc aZirve University, Faculty of Education, Department of Mathematics, Gaziantep, 27260, Turkey bDepartment of Computational and Theoretical Sciences, Faculty of Science, IIUM, 25200 Kuantan, Malaysia cHarran University, Arts and Science Faculty, Department of Mathematics, Sanliurfa, 63120, Turkey

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In this paper, we consider an Ising model with three competing interactions (nearest neighbor, next-nearest neighbor, and ternary prolonged neighbor) on the Cayley tree of order two, investigated by Ganikhodjaev et al. We study translation-invariant Gibbs measures of the Ising model with these competing interactions. Also, we investigate the set of the extreme Gibbs measures called Markov random fields with memory 2 of the model.

DOI: 10.12693/APhysPolA.123.484 PACS numbers: 05.50.+q, 64.60.-i, 64.60.De, 75.10.Hk