Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 66: Poster: Stat. Phys. (Gen., Critical Phen., Biol.)

DY 66.19: Poster

Thursday, March 15, 2018, 15:30–18:00, Poster A

Directed negative-weight percolation — •Christoph Norrenbrock, Mitchell Mkrtchian, and Alexander K. Hartmann — Carl-von-Ossietzky Universität Oldenburg, Oldenburg (Germany)

We consider a directed variant of the negative-weight percolation model [1] in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values. Additionally, in this model variant all edges are directed. For a given realization of the disorder, a minimally weighted loop/path configuration is determined by performing a non-trivial transformation of the original lattice and solving a minimum weight perfect matching problem. For this problem, fast polynomial-time algorithms are available, thus we could study large systems with high accuracy. Depending on the fraction of negatively and positively weighted edges in the lattice, a continuous phase transition can be identified, whose characterizing critical exponents we have estimated by a finite-size scaling analysis of the numerically obtained data. We observe a strong change of the universality class with respect to standard directed percolation, as well as with respect to undirected negative-weight percolation.

[1] Melchert, O. and Hartmann, A. K., New J. Phys. 10 043039 (2008)