The square-triangle random-tiling model in the thermodynamic limit

Abstract

The thermodynamic limit for the square-triangle random-tiling model is considered. The analytic solution of the Bethe-ansatz equations found recently by Widom (1993) is obtained. The analytic expression for entropy density as a function of the fraction of the plane occupied by triangles alpha t is derived for the case alpha t>or= 1/2 , i.e. for the phason gradients having 6-fold symmetry, including 12-fold symmetric phase as the limiting case. The exact values for phason elastic constants are also found.