{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:33:40Z","timestamp":1760240020524,"version":"build-2065373602"},"reference-count":93,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,18]],"date-time":"2019-02-18T00:00:00Z","timestamp":1550448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK1885","HA3169\/3-1"],"award-info":[{"award-number":["GRK1885","HA3169\/3-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2013Loewner Evolution is addressed and recent results for directed NWP are presented.<\/jats:p>","DOI":"10.3390\/e21020193","type":"journal-article","created":{"date-parts":[[2019,2,19]],"date-time":"2019-02-19T04:08:20Z","timestamp":1550549300000},"page":"193","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["From Spin Glasses to Negative-Weight Percolation"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6865-5474","authenticated-orcid":false,"given":"Alexander K.","family":"Hartmann","sequence":"first","affiliation":[{"name":"Institute of Physics, University of Oldenburg, 26111 Oldenburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oliver","family":"Melchert","sequence":"additional","affiliation":[{"name":"Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering\u2014Innovation Across Disciplines), Welfengarten 1, 30167 Hannover, Germany"},{"name":"Institute of Quantum Optics, Leibniz Universit\u00e4t Hannover, Welfengarten 1, 30167 Hannover, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christoph","family":"Norrenbrock","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Oldenburg, 26111 Oldenburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.aop.2005.04.001","article-title":"SLE for theoretical physicists","volume":"318","author":"Cardy","year":"2005","journal-title":"Ann. 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