论文标题
六个vertex模型的固定度量
Stationary measure for six-vertex model on a strip
论文作者
论文摘要
我们在带$$ \ left \ {（x，y）\ in \ mathbb {z}^2：0 \ leq y \ leq x \ leq x \ leq y+n \ right \ right \ right \ right \ right \ right \ right \ right \ right \ right \ right \ right \ right \ right \} $中，研究随机的六个vertex模型。我们基于任何向下路径的三种局部移动的兼容性，开发了一种“矩阵产品ANSATZ”方法来解决其固定度量。水平路径上的固定度量证明是具有两个开放边界的不对称简单排除过程（ASEP）的固定度量的倾斜度。与开放ASEP相似，该倾斜静止度量的统计数据作为位点的数量$ n \ rightarrow \ infty $（带有固定的批量和边界参数）也显示了相位图，这是开放式ASEP相位图的倾斜度。我们以平均粒子密度的限制为例。
We study the stochastic six-vertex model on a strip $$\left\{(x,y)\in\mathbb{Z}^2: 0\leq y\leq x\leq y+N\right\}$$ with two open boundaries. We develop a `matrix product ansatz' method to solve for its stationary measure, based on the compatibility of three types of local moves of any down-right path. The stationary measure on a horizontal path turns out to be a tilting of the stationary measure of the asymmetric simple exclusion process (ASEP) with two open boundaries. Similar to open ASEP, the statistics of this tilted stationary measure as the number of sites $N\rightarrow\infty$ (with the bulk and boundary parameters fixed) also exhibit a phase diagram, which is a tilting of the phase diagram of open ASEP. We study the limit of mean particle density as an example.
