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Arctic curves of the 20V model on a triangle

Mathematical Physics 2023-05-10 v1 Combinatorics math.MP Probability

Abstract

We apply the Tangent Method of Colomo and Sportiello to predict the arctic curves of the Twenty Vertex model with specific domain wall boundary conditions on a triangle, in the Disordered phase, leading to a phase diagram with six types of frozen phases and one liquid one. The result relies on a relation to the Six Vertex model with domain wall boundary conditions and suitable weights, as a consequence of integrability. We also perform the exact refined enumeration of configurations.

Keywords

Cite

@article{arxiv.2212.11129,
  title  = {Arctic curves of the 20V model on a triangle},
  author = {Philippe Di Francesco},
  journal= {arXiv preprint arXiv:2212.11129},
  year   = {2023}
}

Comments

36 pages, 32 figures