Arctic curves of the 20V model on a triangle
arXiv:2212.11129 · doi:10.1088/1751-8121/acccbe
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.
arXiv comment36 pages, 32 figures
References in corpus (14)
- Random Domino Tilings and the Arctic Circle Theorem
- Stochastic six-vertex model
- Arctic curves of the six-vertex model on generic domains: the Tangent Method
- The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime
- The limit shape of large alternating sign matrices
- Arctic curve of the free-fermion six-vertex model in an L-shaped domain
- Algebraic arctic curves in the domain-wall six-vertex model
- A tangent method derivation of the arctic curve for q-weighted paths with arbitrary starting points
- Arctic curves for paths with arbitrary starting points: a tangent method approach
- Arctic Curves in path models from the Tangent Method
- Arctic curves of the twenty-vertex model with domain wall boundaries
- The Arctic curve for Aztec rectangles with defects via the Tangent Method
- Twenty-Vertex model with domain wall boundaries and domino tilings
- Arctic curves of the Reflecting Boundary Six Vertex and of the Twenty Vertex models