Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systemsAxel Kammerer, Felix Höfling and Thomas Franosch
Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Fakultät für Physik, Ludwig-Maximilians-Universität München - Theresienstraße 37, 80333 München, Germany, EU
received 7 November 2008; accepted in final form 20 November 2008; published December 2008
published online 5 December 2008
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our derivation is based on a cluster-resolved scaling theory unifying the scaling of both the cluster size distribution and the dynamics of a random walker. We corroborate our theoretical approach by extensive simulations for a site percolating square lattice and numerically determine both the static and dynamic correction exponents.
64.60.ah - General studies of phase transitions: Percolation.
05.10.-a - Computational methods in statistical physics and nonlinear dynamics.
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