Emptiness formation probability of the six-vertex model and the sixth Painlevé equation

Abstract

We show that the emptiness formation probability of the six-vertex model with domain wall boundary conditions at its free-fermion point is a $\tau$-function of the sixth Painlevé equation. Using this fact we derive asymptotics of the emptiness formation probability in the thermodynamic limit.

48 pages, 3 figures; v2: appendix A and comments at the end of Sect. 4.2 added

References in corpus (4)

• Top eigenvalue of a random matrix: large deviations and third order phase transition
• Third-order phase transition in random tilings
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Cited by in corpus (5)

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• The partition function of the four-vertex model in inhomogeneous external field and trace statistics
• Evaluation of integrals for the emptiness formation probability in the square-ice model
• Thermodynamics of the five-vertex model with scalar-product boundary conditions
• Scaling limit of domino tilings on a pentagonal domain