Numerical entropy and phason elastic constants of plane random tilings with any 2D-fold symmetry

We perform Transition matrix Monte Carlo simulations to evaluate the entropy of rhombus tilings with fixed polygonal boundaries and 2D-fold rotational symmetry. We estimate the large-size limit of this entropy for D=4 to 10. We confirm analytic predictions of [N. Destainville et al., J. Stat. Phys. 120, 799 (2005) and M. Widom et al., J. Stat. Phys. 120, 837 (2005)], in particular that the large size and large D limits commute, and that entropy becomes insensible to size, phason strain and boundary conditions at large D. We are able to infer finite D and finite size scalings of entropy. We also show that phason elastic constants can be estimated for any D by measuring the relevant perpendicular space fluctuations