  We study numerically the geometrical properties of minimally weighted paths
that appear in the negative-weight percolation (NWP) 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 1-rho of bonds
with unit strength and a fraction rho of bond strengths drawn from a Gaussian
distribution with zero mean and unit width. For each such sample, the 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 (GS). A ground state on
such a lattice can be determined performing a non-trivial transformation of the
original graph and applying sophisticated matching algorithms. Here we examine
whether the geometrical properties of the paths are in accordance with
predictions of Schramm-Loewner evolution (SLE). Measuring the fractal dimension
and reviewing Schramm's left passage formula indicates that the paths cannot be
described in terms of SLE.
