Boundary correlation functions of the six and nineteen vertex models with domain wall boundary conditions

TL;DR

This paper derives explicit formulas for boundary correlation functions in six and nineteen vertex models with domain wall boundary conditions, revealing their interrelations and providing a comprehensive analytical framework.

Contribution

It provides the first general expression for boundary correlation functions in the six vertex model and relates nineteen vertex model functions to those of the six vertex model.

Findings

Boundary correlation functions are explicitly expressed for the six vertex model.

Nineteen vertex model boundary functions are derived from six vertex model functions.

Non-boundary correlation functions can be decomposed into boundary correlation functions.

Abstract

Correlation functions of the six and nineteen vertex models on an N \times N lattice with domain wall boundary conditions are studied. The general expression of the boundary correlation functions is obtained for the six vertex model by use of the quantum inverse scattering method. The correlation functions which are not "boundary" can be expressed as a linear sum of the boundary correlation functions. For the nineteen vertex model, the boundary correlation functions are shown to be expressed in terms of those for the six vertex model.