Affiliation: University of Melbourne
Email: T.Guttmann@ms.unimelb.edu.au
Title Of Talk: Self-avoiding walks on non-Euclidean, irregular and quasiperiodic lattices
URL: http://www.ms.unimelb.edu.au/~tonyg/Lectures.html
Abstract: While the behaviour of two-dimensional self-avoiding walks on regular lattices is well understood, and the critical exponents are believed to be exactly known, far less is known about the behaviour of SAW on semi-regular lattices, on non-Euclidean lattices, and on quasiperiodic tilings. For hyperbolic lattices, exact and numerical studies are discussed which show that the critical exponent $\gamma = 1.$ For SAW on the $(3.12^2)$ and $(4.8^2)$ we find the critical exponent is the same as for regular lattices, and give some exact results for the connective constant on one lattice. Finally, recent extensive numerical work on SAW on Ammann-Beenker tilings and Penrose tilings leads to the conclusion that the critical exponent is the same as for regular lattices.
Last update made Mon Mar 17 19:37:01 EST 2003.
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