Dresden 2011 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 40: Posters II
DY 40.37: Poster
Donnerstag, 17. März 2011, 17:00–19:00, P3
Loop length distribution in higher dimensional negative weight percolation — •Gunnar Claussen, Oliver Melchert, and Alexander K. Hartmann — Institut für Physik, Carl-von-Ossietzky-Universität Oldenburg
We consider the negative weight percolation (NWP) problem [1] on large square and cubic lattice graphs, using disorder distributions that allow for edge weights of either sign. We examine loops with negative weight, i.e. percolating and “small” loops, and vary the concentration ρ of negative edge weights. The NWP problem is fundamentally different from conventional percolation problems, e.g. it shows no transitivity, hence there is no simple definition of clusters. Thus, numerical studies on this loop model require a non-trivial transformation of the original graph and the application of sophisticated matching algorithms.
Here, we study the problem by numerical methods [2]. The phenomenon is examined for ρ≤ρc, the critical point. We characterize the ensemble of “small” loops by the Fisher exponent τ, which describes the distribution of loop lengths at ρ through nρ(l)∼ l−τ e−TL l, and by the loop-size cut-off exponent σ, which determines the line tension TL by TL∼|ρ−ρc|1/σ. We compare our results to previous finite-size scaling analyses [3].
O. Melchert and A.K. Hartmann, New J. Phys. 10 (2008) 043039
A.K. Hartmann, Practical Guide to Computer Simulations, World Scientific (2009)
O. Melchert, L. Apolo and A.K. Hartmann, Phys. Rev. E 81 (2010) 051108