论文标题
五位vertex模型的决定符公式
Determinant formulas for the five-vertex model
论文作者
论文摘要
我们考虑具有固定边界条件的有限正方形晶格上的五个vertex模型，以使模型的配置与盒装平面分区一对一（3D Young图，适合给定尺寸的盒子）。不均匀模型的分区函数是根据决定因素给出的。对于同质模型，可以根据汉克尔的决定因素给出。我们还表明，在同质情况下，分区函数是第六次painlevé方程相对于重量的快速变量的$τ$。
We consider the five-vertex model on a finite square lattice with fixed boundary conditions such that the configurations of the model are in a one-to-one correspondence with the boxed plane partitions (3D Young diagrams which fit into a box of given size). The partition function of an inhomogeneous model is given in terms of a determinant. For the homogeneous model, it can be given in terms of a Hankel determinant. We also show that in the homogeneous case the partition function is a $τ$-function of the sixth Painlevé equation with respect to the rapidity variable of the weights.
