2020/11/30 by Ivan N. Burenev, Andrei G. Pronko
Physics and Astronomy · Mathematics · #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/abd785
published as J. Phys. A: Math. Theor. 54 (2021), 055008 · 32 pages, 5 figures; v2: misprints corrected
arxiv created 2020/12/24 · arxiv updated 2021/02/23
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.