Emptiness formation probability of the six-vertex model and the sixth Painlev\'e equation

TL;DR

This paper demonstrates that the emptiness formation probability in the six-vertex model at the free-fermion point is a tau-function of the sixth Painlevé equation, enabling the derivation of its asymptotic behavior.

Contribution

It establishes a novel connection between the six-vertex model's emptiness formation probability and the sixth Painlevé equation, providing new analytical tools.

Findings

Emptiness formation probability is a tau-function of the sixth Painlevé equation.

Asymptotic behavior of the probability is derived in the thermodynamic limit.

The connection enables precise asymptotic analysis of the model.

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 Painlev\'e equation. Using this fact we derive asymptotics of the emptiness formation probability in the thermodynamic limit.