Arctic curves of the twenty-vertex model with domain wall boundaries (Q1987629)

The authors consider the so-called twenty-vertex (20V) model which is an alternative denomination for the ice model on the regular triangular lattice. They get an explicit expression for the location of the arctic curve of the 20V model with domain wall boundary conditions (DWBC) 1 or 2. The authors derive the predictions of the tangent method for the arctic curve of the 20V model with DWBC1 or DWBC2. Also, the authors obtain a direct correspondence between the 20V model and a single, properly weighted, 6V model with DWBC. Then, the authors obtain the large-\(n\) asymptotics of the 20V model one-point function, a crucial ingredient in the computation of the arctic curve. The authors present the implementation of the tangent method in a simple case where the vertex weights depend on a single quantum parameter. An alternative set of paths describing the 20V model configurations is described. The arctic curve for the general case of given weights is derived. The authors give a number of plots to illustrate the evolution of the arctic curve with varying \(\eta\), \(\lambda\) and \(\mu\). They present numerical simulations for large typical 20V model configurations. In the last section, they study the arctic curve for the quarter turn symmetric holey aztec domino tiling model (QTHADT). The arctic curve of the given model is analyzed.