Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 29: Posters II
DY 29.13: Poster
Thursday, March 29, 2012, 17:00–19:00, Poster A
Loop length distributions in the Negative Weight Percolation (NWP) problem: Extension to 4 to 7 dimensions — •Gunnar Claußen, Oliver Melchert, and Alexander K. Hartmann — Institut für Physik, Carl-von-Ossietzky-Universität Oldenburg
The negative weight percolation (NWP) problem [1] on hypercubic lattice graphs is a bond percolation problem with disorder distributions that allow for edge weights of either sign. Under variation of the concentration ρ of negative edge weights “small” and percolating loops of total negative weight are found. The NWP problem shows no transitivity and has no simple definition of clusters, therefore it fundamentally differs from conventional percolation problems. A numerical examination of the models requires a sophisticated transformation of the original graph and the application of matching algorithms in order to find the minimum-weighted configuration of loops.
Here, we study the problem by numerical methods for ρ below the critical point ρc, where system-spanning loops appear. The core of the examination is the determination of the Fisher exponent τ, which describes the loop length distribution according to n(l)∝ l−τ, and the loop-size cut-off exponent σ. The latter determines the line tension TL of the non-pecolating loops by TL(ρ)∝|ρ−ρc|1/σ and complies to a cut-off in loop lengths for ρ < ρc. In extension of previous works the model is examined for dimensions d=4...7. The results are compared to previous finite-size scaling analyses [2].
O. Melchert and A.K. Hartmann, New J. Phys. 10 (2008) 043039
O. Melchert, L. Apolo and A.K. Hartmann, PRE 81 (2010) 051108