From Spin Glasses to Negative-Weight Percolation

authored by: Alexander K. Hartmann, Oliver Melchert, Christoph Norrenbrock
Abstract: Spin glasses are prototypical random systems modelling magnetic alloys. One important way to investigate spin glass models is to study domain walls. For two dimensions, this can be algorithmically understood as the calculation of a shortest path, which allows for negative distances or weights. This led to the creation of the negative weight percolation (NWP) model, which is presented here along with all necessary basics from spin glasses, graph theory and corresponding algorithms. The algorithmic approach involves a mapping to the classical matching problem for graphs. In addition, a summary of results is given, which were obtained during the past decade. This includes the study of percolation transitions in dimension from d = 2 up to and beyond the upper critical dimension d_u = 6, also for random graphs. It is shown that NWP is in a different universality class than standard percolation. Furthermore, the question of whether NWP exhibits properties of Stochastic-Loewner Evolution is addressed and recent results for directed NWP are presented.
Organisation(s): PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
Institute of Quantum Optics
External Organisation(s): Carl von Ossietzky University of Oldenburg
Type: Review article
Journal: Entropy
Volume: 21
ISSN: 1099-4300
Publication date: 02.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Information Systems, Mathematical Physics, Physics and Astronomy (miscellaneous), Electrical and Electronic Engineering
Electronic version(s): https://doi.org/10.3390/e21020193 (Access: Open)
https://doi.org/10.15488/10963 (Access: Open)