LEITER TO THE EDITOR Finite-size scaling amplitudes in a random tiling model

Abstract. We study finite-size corrections to the free energy in a two-dimensional random tiling model. This model is equivalent to an asymmetric six-vertex model and exhibits commensurate-incommensurate phase transitions of the Pokrovsky-Talapov type. We calculate finite-size scaling amplitudes of the free energy inside the incommensurate phase, analytically and numerically, by employing a transfer matrix method. Both periodic and free boundary conditions are considered. These amplitudes are consistent with predictions of the theory of conformal invariance with the conformal charge c = 1. Tiling models describing quasicrystals have received a considerable amount of attention recently [ 1-51. Experimentally some rapidly quenched alloys were found to have non-crystallographic symmetries with rather sharp diffraction peaks [ 6]. Recent experi-ments on AlCuFe [7,8] revealed diffraction peaks whose width is resolution limited, indicating long range quasiperiodic translational order coexisting with icosahedral bond orientational order. The Penrose tiling, which consists of two types of rhombi tiled together with strong matching rules, is perfectly quasiperiodic and exhibits a Bragg diffraction pattern with a non-crystallographic five-fold symmetry [2]. Penros