The genus-zero five-vertex model

Kenyon, Richard L.; Prause, István

doi:10.48550/arxiv.2101.04195

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2021

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“…Recently, a notable progress had been achieved in understanding scaling properties of the five-vertex model in a rather general setup by variational methods, with the focus on phase separation and limit shape phenomena [12][13][14][15]. On the other hand, for the case of scalar-product boundary conditions an important problem consists in constructing expansions of the partition function in the limit of large system size.…”

Section: Introductionmentioning

confidence: 99%

Determinant formulas for the five-vertex model

Burenev¹,

Pronko²

2021

J. Phys. A: Math. Theor.

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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.

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Section: Introductionmentioning

confidence: 99%