Abstract
We study numerically the geometrical properties of minimally weighted paths that appear in the minimally weighted path (MWP) model on two-dimensional lattices assuming a combination of periodic and free boundary conditions (BCs). Each realization of the disorder consists of a random fraction of bonds with unit strength and a fraction of bond strengths drawn from a Gaussian distribution with zero mean and unit width. For each such sample, a path is forced to span the lattice along the direction with the free BCs. The path and a set of negatively weighted loops form a ground state. A ground state on such a lattice can be determined performing a nontrivial transformation of the original graph and applying sophisticated matching algorithms. Here we examine whether the geometrical properties of the paths are in accordance with the predictions of the Schramm-Loewner evolution (SLE). Measuring the fractal dimension, considering the winding angle statistics, and reviewing Schramm's left passage formula indicate that the paths cannot be described in terms of SLE.
2 More- Received 11 May 2012
DOI:https://doi.org/10.1103/PhysRevE.87.032142
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