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

Hasan Akın
2018 International Journal of Modern Physics C  
In this paper, we consider the Ising-Vanniminus model on an arbitrary order Cayley tree. We generalize the results conjectured in [Chinese Journal of Physics, 54 (4), 635-649 (2016)] and [International Journal of Modern Physics, arXiv:1608.06178] for an arbitrary order Cayley tree. We establish existence and a full classification of translation invariant Gibbs measures with memory of length 2 associated with the model on arbitrary order Cayley tree. We construct the recurrence equations
more » ... nding generalized ANNNI model. We satisfy the Kolmogorov consistency condition. We propose a rigorous measure-theoretical approach to investigate the Gibbs measures with memory of length 2 for the model. We explain whether the number of branches of tree does not change the number of Gibbs measures. Also we take up with trying to determine when phase transition does occur.
doi:10.1142/s012918311850016x fatcat:hccxy3556fbv5b6gcfxf4zhbka