Berlin 2008 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 1: Critical phenomena and phase transitions

DY 1.4: Talk

Monday, February 25, 2008, 11:00–11:15, MA 004

Negative-weight percolation — •Oliver Melchert and Alexander K. Hartmann — Institut für Physik, Universität Oldenburg, 26111 Oldenburg

We describe a percolation problem on lattices, with edge weights drawn from disorder distributions that allow for weights of either sign, i.e. including negative weights. We are interested whether there are spanning paths or loops of total negative weight. This kind of percolation problem is fundamentally different from conventional percolation problems, e.g. it does not exhibit transitivity, hence no simple definition of clusters, and several spanning paths/loops might coexist in the percolation regime at the same time. To study this percolation problem numerically, one has to perform a non-trivial transformation of the original graph and apply sophisticated matching algorithms.

Here, we study the corresponding percolation transitions on large square and cubic lattices for two types of disorder distributions and determine the critical exponents. The results show that negative-weight percolation is in a different universality class compared to conventional bond/site percolation. On the other hand, negative-weight percolation seems to be related to the ferromagnet/spin-glass transition of random-bond Ising systems, at least in two dimensions.