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

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  • N. Destainville

Abstract

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Suggested Citation

  • N. Destainville, 2006. "Numerical entropy and phason elastic constants of plane random tilings with any 2D-fold symmetry," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 52(1), pages 119-123, July.
    • Handle: RePEc:spr:eurphb:v:52:y:2006:i:1:p:119-123
    DOI: 10.1140/epjb/e2006-00263-1
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