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

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

preprint2016arXivOpen access
A. V. KitaevA. G. Pronko
math-phmath.MP
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A. V. KitaevA. G. Pronko

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