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

2000/08/23 by V. Korepin, Korepin, V., P. Zinn-Justin +1
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0008030

arxiv created 2000/08/23 · arxiv updated 2009/11/30

Abstract

In this note, we consider the six-vertex model with domain wall boundary conditions, defined on a M× M lattice, in the inhomogeneous case where the partition function depends on 2M inhomogeneities λ_j and μ_k. For a particular choice of the set of λ_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.

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