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Emptiness Formation Probability of the Six-Vertex Model and the Sixth Painlevé Equation

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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.

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Authors and Affiliations

  1. V. A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia

    A. V. Kitaev & A. G. Pronko

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  1. A. V. Kitaev
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  2. A. G. Pronko
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Correspondence to A. G. Pronko.

Additional information

Communicated by H. Spohn

This work is partially supported by the Russian Foundation for Basic Research, Grant No. 13-01-00336.

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Kitaev, A.V., Pronko, A.G. Emptiness Formation Probability of the Six-Vertex Model and the Sixth Painlevé Equation. Commun. Math. Phys. 345, 305–354 (2016). https://doi.org/10.1007/s00220-016-2636-5

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