Self-avoiding walks and polygons on quasiperiodic tilings
Rogers AN, Richard C, Guttmann A (2003)
Publication Type: Journal article
Publication year: 2003
Journal
Publisher: Iop Publishing Ltd
Book Volume: 36
Pages Range: 6661-6673
Journal Issue: 24
DOI: 10.1088/0305-4470/36/24/305
Abstract
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 initial vertex. We compare different ways of counting and demonstrate that suitable averaging improves convergence 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 enumeration data do not allow us to draw decisive conclusions about the exponent.
Authors with CRIS profile
Involved external institutions
Australia (AU)How to cite
APA:
Rogers, A.N., Richard, C., & Guttmann, A. (2003). Self-avoiding walks and polygons on quasiperiodic tilings. Journal of Physics A: Mathematical and General, 36(24), 6661-6673. https://dx.doi.org/10.1088/0305-4470/36/24/305
MLA:
Rogers, A. N., Christoph Richard, and Anthony Guttmann. "Self-avoiding walks and polygons on quasiperiodic tilings." Journal of Physics A: Mathematical and General 36.24 (2003): 6661-6673.
BibTeX: Download