Integral representation of the correlations around a vertex of the six-vertex model

We study exact solutions of the four-point correlation functions around a vertex of the antiferroelectric six-vertex model. After showing that an expression for the correlations is readily obtained by differentiating the known exact solution of the free energy, we present a new expression for the correlations derived through the recently developed vertex operator approach. It has the form of a double contour integral of a meromorphic function. To give a new verification of the vertex operator approach beyond the case of the one-point function: we prove the equality of the two expressions by calculating the contour integrals.