On Ground States and Phase Transitions of $\lambda$-Model on the Cayley Tree

Farrukh Mukhamedov; Chin Hee Pah; Hakim Jamil

On Ground States and Phase Transitions of $\lambda$-Model on the Cayley Tree

Mathematical Physics 2017-08-15 v1 Statistical Mechanics math.MP

Authors: Farrukh Mukhamedov , Chin Hee Pah , Hakim Jamil

Abstract

In the paper, we consider the $\lambda$ -model with spin values $\{1, 2, 3\}$ on the Cayley tree of order two. We first describe ground states of the model. Moreover, we also proved the existence of translation-invariant Gibb measures for the $\lambda$ -model which yield the existence of the phase transition. Lastly, we established the exitance of 2-periodic Gibbs measures for the model.

Keywords

lambda model Cayley tree ground states phase transition Gibbs measures translation invariance 2-periodic Gibbs measures

Cite

@article{arxiv.1610.07019,
  title  = {On Ground States and Phase Transitions of $\lambda$-Model on the Cayley Tree},
  author = {Farrukh Mukhamedov and Chin Hee Pah and Hakim Jamil},
  journal= {arXiv preprint arXiv:1610.07019},
  year   = {2017}
}

Comments

20 pages, 17 figures

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