Scale-free enumeration of self-avoiding walks on critical percolation clusters
Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig Postfach 100920, D-04009 Leipzig, Germany, EU
Received: 6 May 2012
Accepted: 17 July 2012
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. We have implemented the method in 2D and used it 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 can be used to check and gauge other methods, analytical and numerical. It can be adapted to higher dimensions and might also be extended to similar systems.
PACS: 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.) / 36.20.-r – Macromolecules and polymer molecules / 64.60.ah – Percolation
© EPLA, 2012