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2013 | 123 | 2 | 484-487
Article title

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

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EN
Abstracts
EN
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.
Keywords
Year
Volume
123
Issue
2
Pages
484-487
Physical description
Dates
published
2013-02
References
  • [1] J.W. Gibbs, Elementary Principles in Statistical Mechanics, Yale University Press, New Haven 1902
  • [2] L. Boltzmann, Lectures on the Theory of Gases, Gauthier-Villars, Paris, tome I 1902, tome II 1905, reedition Jean Gabay, Paris 1987 (in French)
  • [3] N. Ganikhodjaev, H. Akın, S. Uğuz, S. Temir, J. Concrete Appl. Math. 9, 26 (2011)
  • [4] N. Ganikhodjaev, H. Akın, S. Uğuz, S. Temir, Phase Transit. 84, 1045 (2011)
  • [5] N. Ganikhodjaev, H. Akın, S. Uğuz, S. Temir, J. Stat. Mech. 2011, P03025 (2011)
  • [6] J. Vannimenus, Z. Phys. B 43, 141 (1981)
  • [7] M. Fannes, A. Verbeure, Commun. Math. Phys. 96, 115 (1984)
  • [8] H.O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter Stud. Math., Vol. 9, Walter de Gruyter, Berlin 1988
  • [9] Ch.J. Preston, Gibbs States on Countable Sets, Cambridge Univ. Press, Cambridge 1974
  • [10] F. Spitzer, Ann. Probab. 3, 387 (1975)
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv123n2107kz
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