THE SQUARE-TRIANGLE RANDOM-TILING MODEL IN THE THERMODYNAMIC LIMIT

The thermodynamic limit for the square-triangle random-tiling model is considered. The analytic solution of the Bethe-ansatz equations found recently by Widom 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) greater-than-or-equal-to 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.