Berlin 2012 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Posters I

DY 22.9: Poster

Mittwoch, 28. März 2012, 17:00–19:00, Poster A

Scale-free enumeration of self-avoiding walks on critical percolation clusters — •Niklas Fricke and Wolfhard Janke — Institut für Theoretische Physik, Universität Leipzig, Germany

We present a new method for exact enumeration of self-avoiding walks on critical percolation clusters. It can handle very long walks by exploiting the clusters’ low connectivity and self-similarity. In 2D we were able to enumerate walks of more than 1000 steps with over 10¹⁷⁰ conformations. The exponents ν and γ, governing the scaling behavior of the end-to-end distance and the number of configurations, as well as the connectivity constant µ could thus be determined with unprecedented accuracy. The method will help answering long-standing questions regarding this particular problem and might be extended to similar systems. Furthermore, it can be used to check and gauge other methods, analytical and numerical.