Hard-hexagon model: Calculation of anisotropic interfacial tension from asymptotic degeneracy of largest eigenvalues of row-row transfer matrix

Abstract

To find the directional dependence of the interfacial tension of the hard-hexagon model, an inhomogeneous system is studied. This system is defined on a square lattice with (1+v)M columns so that the lhs of the (M+1)th column is the hard-hexagon model and the rhs of the (M+1)th column works as the operator which shifts the particle configuration of a column downward. A triplet of the largest eigenvalues of the row-row transfer matrix are asymptotically degenerate asM→∞ under the conditions that (1−v)M≡0 (mod 3), withv being fixed to be constant. The interfacial tension of a tilted interface is calculated from the finite correction terms in this limit.