BETHE ANSATZ SOLUTION OF THE SQUARE-TRIANGLE RANDOM TILING MODEL

Random tiling models cover the plane with a set of rigid tiles without gaps between tiles and without overlap. This paper considers tilings of the plane by squares and equilateral triangles which display twelvefold rotational symmetry and quasi-long-range quasiperiodic translational order. Tiling configurations may be described as networks of interacting domain walls, for which the Bethe ansatz provides the exact (formal) partition function. Numerical evaluation yields the entropy and phason elastic constants with high accuracy.