Generalized emptiness formation probability in the six-vertex model

TL;DR

This paper extends the concept of emptiness formation probability in the six-vertex model to include arbitrary Young diagram shapes, providing a multiple integral representation for this generalized correlation function.

Contribution

It introduces a generalized emptiness formation probability for arbitrary Young diagram shapes and derives a multiple integral formula for it.

Findings

Provides a new integral representation for the generalized probability.

Extends the understanding of frozen regions in the six-vertex model.

Enables analysis of more complex frozen configurations.

Abstract

In the six-vertex model with domain wall boundary conditions, the emptiness formation probability is the probability that a rectangular region in the top left corner of the lattice is frozen. We generalize this notion to the case where the frozen region has the shape of a generic Young diagram. We derive here a multiple integral representation for this correlation function.