Self-avoiding walks and polygons on quasiperiodic tilings

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dc.creatorRogers, A. N.
dc.creatorRichard, C.
dc.creatorGuttmann, A. J.
dc.date2003-02-20
dc.date2004-05-19
dc.date.accessioned2026-07-07T09:58:44Z
dc.date.available2026-07-07T09:58:44Z
dc.descriptionWe 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.
dc.description17 pages, 12 figures. v2: minor changes, version as published
dc.identifierhttps://arxiv.org/abs/cond-mat/0302414
dc.identifierhttp://arxiv.org/abs/cond-mat/0302414
dc.identifierJ. Phys. A 36 (2003), 6333-6345
dc.identifierdoi:10.1088/0305-4470/36/24/305
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167823
dc.subjectStatistical Mechanics
dc.titleSelf-avoiding walks and polygons on quasiperiodic tilings
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