# Inhomogeneous Six-Vertex Model with Domain Wall Boundary Conditions and Bethe Ansatz

### Vladimir Korepin 1, Paul Zinn-Justin 1

#### Journal of Mathematical Physics 43 (2002) 3261-3267

In this note, we consider the six-vertex model with domain wall boundary conditions, defined on a $M\times M$ lattice, in the inhomogeneous case where the partition function depends on 2M inhomogeneities $\lambda_j$ and $\mu_k$. For a particular choice of the set of $\lambda_j$ we find a new determinant representation for the partition function, which allows evaluation of the bulk free energy in the thermodynamic limit. This provides a new connection between two types of determinant formulae. We also show in a special case that spin correlations on the horizontal line going through the center coincide with the ones for periodic boundary conditions.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE),
CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot