Negative-weight percolation

O Melchert, AK Hartmann - New Journal of Physics, 2008 - iopscience.iop.org
… We have introduced a percolation problem, … percolating if spanning loops or paths of negative
weight exist. Hence, this model might be fundamentally different from classical percolation

Phase transitions in diluted negative-weight percolation models

L Apolo, O Melchert, AK Hartmann - … Review E—Statistical, Nonlinear, and Soft …, 2009 - APS
… In the past decades, a large number of percolationnegative-weight percolation NWP,
a problem in similar vein but with subtle differences compared to other stringlike percolation

Upper critical dimension of the negative-weight percolation problem

O Melchert, L Apolo, AK Hartmann - … Review E—Statistical, Nonlinear, and Soft …, 2010 - APS
… lattices prepared at the percolation threshold of 2D random percolation and at full disorder,
the … Here, we study the negative-weight percolation problem on hypercubic lattice graphs in …

Negative-weight percolation: review of existing literature and scaling behavior of the path weight in 2d

O Melchert, C Norrenbrock, AK Hartmann - Physics Procedia, 2014 - Elsevier
… We consider the negative weight percolation (NWP) problem … the full ensemble of loops
with negative weight, ie non-trivial (… spanning loops of total negative weight. For the numerical …

Mean-field behavior of the negative-weight percolation model on random regular graphs

O Melchert, AK Hartmann, M Mézard - … E—Statistical, Nonlinear, and Soft Matter …, 2011 - APS
… , geometric observables and scaling concepts similar to those used in percolation theory [16…
This paper studies the negative-weight percolation (NWP) problem [20–22], wherein one …

Directed negative-weight percolation

C Norrenbrock, MM Mkrtchian, AK Hartmann - Physical Review E, 2019 - APS
… We consider the negative-weight percolation model on directed graphs. In particular, we …
standard directed percolation as well as with respect to undirected negative-weight percolation. …

Analysis of the loop length distribution for the negative-weight percolation problem in dimensions through

G Claussen, L Apolo, O Melchert, AK Hartmann - Physical Review E—Statistical …, 2012 - APS
… We consider the negative weight percolation (NWP) problem … the full ensemble of loops
with negative weight, ie, nontrivial (… spanning loops of total negative weight. While previous …

Is negative-weight percolation compatible with SLE?

C Norrenbrock, O Melchert, AK Hartmann - arXiv preprint arXiv:1205.1412, 2012 - arxiv.org
… Such paths can be as simple as boundaries of percolation clus… Basic problems like percolation
or domain walls in Ising … In this article we study paths in the negative-weight percolation (…

From Spin Glasses to Negative-Weight Percolation

AK Hartmann, O Melchert, C Norrenbrock - Entropy, 2019 - mdpi.com
… This led to the creation of the negative weight percolation (… This includes the study of
percolation transitions in dimension … Since negative-weight percolation is a model of paths, next, …

Configurational statistics of densely and fully packed loops in the negative-weight percolation model

O Melchert, AK Hartmann - The European Physical Journal B, 2011 - Springer
… of loops in the negative-weight percolation (NWP) model. In … similar to those used in percolation
studies and perform finite-… studied behavior at the percolation threshold, where random-…