Self-avoiding walks and polygons on quasiperiodic tilings

Details Self-avoiding walks and polygons on quasiperiodic tilings Self-avoiding walks and polygons on quasiperiodic tilings

2003-02-20

arxiv.org/abs/cond-mat/0302414v2

J. Phys. A 36 (2003), 6333-6345

Physics

Condensed Matter

Statistical Mechanics

17 pages, 12 figures. v2: minor changes, version as published

Scientific paper

10.1088/0305-4470/36/24/305

We enumerate self-avoiding walks and polygons, counted by perimeter, on the quasiperiodic rhombic Penrose and Ammann-Beenker tilings, thereby considerably extending previous results. In contrast to similar problems on regular lattices, these numbers depend on the chosen start vertex. We compare different ways of counting and demonstrate that suitable averaging improves converge to the asymptotic regime. This leads to improved estimates for critical points and exponents, which support the conjecture that self-avoiding walks on quasiperiodic tilings belong to the same universality class as self-avoiding walks on the square lattice. For polygons, the obtained e numeration data does not allow to draw decisive conclusions about the exponent.

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