The emptiness formation probability, and representations for nonlocal correlation functions, of the 20-vertex model

TL;DR

This paper investigates the emptiness formation probability and nonlocal correlation functions of the 20-vertex model, extending methods from the 6-vertex model and deriving new integral representations.

Contribution

It introduces a contour integral representation for nonlocal correlations and a new emptiness formation probability concept for the 20-vertex model.

Findings

Derived a contour integral representation for nonlocal correlations.

Introduced a counterpart of the emptiness formation probability for the 20-vertex model.

Extended existing methods from the 6-vertex model to the 20-vertex model.

Abstract

We study the emptiness formation probability, along with various representations for nonlocal correlation functions, of the 20-vertex model. In doing so, we leverage previous arguments for representations of nonlocal correlation functions for the 6-vertex model, under domain-wall boundary conditions, due to Colomo, Di Giulio, and Pronko, in addition to the inhomogeneous, and homogeneous, determinantal representations for the 20-vertex partition function due to Di Francesco, also under domain-wall boundary conditions. By taking a product of row configuration probabilities, we obtain a desired contour integral representation for nonlocal correlations from a determinantal representation. Finally, a counterpart of the emptiness formation probability is introduced for the 20-vertex model.