# Directed negative-weight percolation

## TL;DR

This paper studies a directed negative-weight percolation model on a 2D lattice, revealing a phase transition with a different universality class from standard directed percolation, using polynomial algorithms for large systems.

## Contribution

It introduces a directed variant of negative-weight percolation and analyzes its critical behavior with finite-size scaling, highlighting a new universality class.

## Key findings

- Identified a continuous phase transition in the model.
- Estimated critical exponents via finite-size scaling.
- Found a change in universality class compared to standard directed percolation.

## Abstract

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.