Gibbs measures with memory of length 2 on an arbitrary-order Cayley tree

Hasan Akın ()
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Hasan Akın: Ceyhun Atuf Kansu Caddesi 1164, Sokak 9/4, TR06105, Çankaya, Ankara, Turkey

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 02, 1-21

Abstract: In this paper, we consider the Ising-Vanniminus model on an arbitrary-order Cayley tree. We generalize the results conjectured by Akın [Chinese J. Phys. 54(4), 635–649 (2016) and Int. J. Mod. Phys. B 31(13), 1750093 (2017)] for an arbitrary-order Cayley tree. We establish the existence and a full classification of translation-invariant Gibbs measures (TIGMs) with a memory of length 2 associated with the model on arbitrary-order Cayley tree. We construct the recurrence equations corresponding to the generalized ANNNI model. We satisfy the Kolmogorov consistency condition. We propose a rigorous measure-theoretical approach to investigate the Gibbs measures with a memory of length 2 for the model. We explain if the number of branches of the tree does not change the number of Gibbs measures. Also, we try to determine when the phase transition does occur.

Keywords: Solvable lattice models; rigorous results in statistical mechanics; Gibbs measures; Ising–Vannimenus model; phase transition (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S012918311850016X

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