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Entropy 2019, 21(2), 193; https://doi.org/10.3390/e21020193

From Spin Glasses to Negative-Weight Percolation

1
Institute of Physics, University of Oldenburg, 26111 Oldenburg, Germany
2
Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering—Innovation Across Disciplines), Welfengarten 1, 30167 Hannover, Germany
3
Institute of Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
*
Author to whom correspondence should be addressed.
Received: 22 January 2019 / Revised: 12 February 2019 / Accepted: 13 February 2019 / Published: 18 February 2019
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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. View Full-Text
Keywords: disordered systems; frustration; phase transition; optimisation; negative weight percolation disordered systems; frustration; phase transition; optimisation; negative weight percolation
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Hartmann, A.K.; Melchert, O.; Norrenbrock, C. From Spin Glasses to Negative-Weight Percolation. Entropy 2019, 21, 193.

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