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arXiv · 2011.01972

Determinant formulas for the five-vertex model

Ivan N. Burenev·Andrei G. Pronko
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Abstract

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 $\tau$-function of the sixth Painlev\'e equation with respect to the rapidity variable of the weights.

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Ivan N. Burenev, Andrei G. Pronko. 2020-11-03. Determinant formulas for the five-vertex model. https://doi.org/10.1088/1751-8121%2Fabd785

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