反铁电畴壁六顶点模型的北极曲线

Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles

Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex ($6$V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a $s\times n$ square lattice ($s\leq n$). In this paper, we derive the analytic expression of the arctic curve, for $a=b=1$ and $c=\sqrt{2}$ ($Δ=0$), while keeping the ratio $s/n \,\in [0,1]$ as a free parameter. The computation relies on the tangent method. We also consider domino tilings of double Aztec rectangles and show via the tangent method …

四顶点模型的北极曲线

Arctic curves of the four-vertex model

本文研究具有特殊固定边界条件的四顶点模型，利用切线法和基于Hahn多项式正交化测度的关联函数严格推导出分隔无序区域与六个冻结角的北极曲线解析表达式，并证明其涨落服从Tracy-Widom分布。