  We consider a directed variant of the negative-weight percolation model in a
two-dimensional, periodic, square lattice. The problem exhibits edge weights
which are taken from a distribution that allows for both positive and negative
values. Additionally, in this model variant all edges are directed. For a given
realization of the disorder, a minimally weighted loop/path configuration is
determined by performing a non-trivial transformation of the original lattice
into a minimum weight perfect matching problem. For this problem, fast
polynomial-time algorithms are available, thus we could study large systems
with high accuracy. Depending on the fraction of negatively and positively
weighted edges in the lattice, a continuous phase transition can be identified,
whose characterizing critical exponents we have estimated by a finite-size
scaling analyses of the numerically obtained data. We observe a strong change
of the universality class with respect to standard directed percolation, as
well as with respect to undirected negative-weight percolation. Furthermore,
the relation to directed polymers in random media is illustrated.
