Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees

N. N. Ganikhodjaev; N. M. Khatamov; U. A. Rozikov

Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees

Mathematical Physics 2023-09-21 v2 math.MP

Authors: N. N. Ganikhodjaev , N. M. Khatamov , U. A. Rozikov

Abstract

The work is devoted to gradient Gibbs measures (GGMs) of a SOS model with countable set $\mathbb Z$ of spin values and having alternating magnetism on Cayley trees. This model is defined by a nearest-neighbor gradient interaction potential. Using K\"ulske-Schriever argument, based on boundary law equations, we give several $q$ -height-periodic translations invariant GGMs for $q=2,3,4$ .

Keywords

gradient gibbs measures sos model alternating magnetism cayley trees boundary law height-periodic translations

Cite

@article{arxiv.2206.00245,
  title  = {Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees},
  author = {N. N. Ganikhodjaev and N. M. Khatamov and U. A. Rozikov},
  journal= {arXiv preprint arXiv:2206.00245},
  year   = {2023}
}

Comments

12 pages, 1 figure

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