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

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

2006-06-13

arxiv.org/abs/cond-mat/0606329v1

Eur. Phys. J. B 52, 119 (2006).

Physics

Condensed Matter

Statistical Mechanics

Accepted for publication in Eur. Phys. J. B

Scientific paper

10.1140/epjb/e2006-00263-1

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.

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