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DY: Fachverband Dynamik und Statistische Physik

DY 40: Posters II

DY 40.33: Poster

Thursday, March 17, 2011, 17:00–19:00, P3

Examining the SLE properties of paths in the negative-weight percolation model — •Christoph Norrenbrock, Oliver Melchert, and Alexander K. Hartmann — Institut für Physik, Carl-von-Ossietzky Universität Oldenburg, Oldenburg (Germany)

We consider lattice spanning paths of total negative weight on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. Each realization of the disorder consists of a random fraction (1−ϕ) of bonds with unit strength and a fraction ϕ of bonds drawn from a Gaussian distribution with zero mean and unit width. This negative-weight percolation (NWP) problem is fundamentally different from conventional percolation [1]. To investigate this percolation problem by means of numerical simulations [2], one has to perform a non-trivial transformation of the original graph and apply sophisticated matching algorithms.

Here we study whether the geometry of these paths can be described in terms of Schramm-Loewner evolution. We exhibit that the paths do not verify the prediction of Schramm’s "left passage formula" [3].
 Melchert, O. and Hartmann, A. K., New. J. Phys. 10 (2008) 043039
 Hartmann, A. K., Practical guide to computer simulations (World Scientific, 2009)
 Schramm, O., Electr. Comm. Prob. 6 (2001)