Configurational statistics of densely and fully packed loops in the negative-weight percolation model
By means of numerical simulations we investigate the configurational properties of densely and fully packed configurations of loops in the negative-weight percolation (NWP) model. In the presented study we consider 2d square, 2d honeycomb, 3d simple cubic and id hypereubic lattice graphs, where edge weights are drawn from a Gaussian distribution. For a given realization of the disorder we then compute a configuration of loops, such that the configurational energy, given by the sum of all individual loop weights, is minimized. For this purpose, we employ a mapping of the NWP model to the minimum-weight perfect matching problem that ran be solved exactly by using sophisticated polynomial-time matching algorithms. We characterize the loops via observables similar to those used in percolation studies aud perform finite-size scaling analyses, up to side length L=256 in 2d, L=48 in 3d and L=20 in 4d (for which we study only some observables), in order to estimate geometric exponents that characterize the configurations of densely and fully packed loops. One major result is that the loops behave like uncorrelated random walks from dimension d=3 on. in contrast to the previously studied behavior at the percolation threshold, where random-walk behavior is obtained for d ≥ 6.
O. Melcbert A. K. Hartmann
Iustitut fuer Physik, Univenutaet Oldenburg, Carl-von-Ossietzky Strasse, 26111 Oldenburg. Germany
国际会议
International Workshop on Statistical Physics and Computer Sciences(统计物理与计算机科学交叉研究国际研讨会 )
北京
英文
42-52
2010-07-08（万方平台首次上网日期，不代表论文的发表时间）