Hartmann Alexander K, Melchert Oliver, Norrenbrock Christoph
Institute of Physics, University of Oldenburg, 26111 Oldenburg, Germany.
Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering-Innovation Across Disciplines), Welfengarten 1, 30167 Hannover, Germany.
Entropy (Basel). 2019 Feb 18;21(2):193. doi: 10.3390/e21020193.
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.
自旋玻璃是模拟磁性合金的典型随机系统。研究自旋玻璃模型的一种重要方法是研究畴壁。对于二维情况，这在算法上可理解为最短路径的计算，其中允许存在负距离或权重。这导致了负权重渗流（NWP）模型的创建，本文将介绍该模型以及自旋玻璃、图论和相应算法的所有必要基础知识。算法方法涉及到与图的经典匹配问题的映射。此外，还给出了过去十年中获得的结果总结。这包括对维度从d = 2到直至并超过上临界维度d u = 6的渗流转变的研究，随机图的情况也包括在内。结果表明，NWP与标准渗流处于不同的普适类。此外，还讨论了NWP是否表现出随机洛厄纳演化特性的问题，并给出了有向NWP的最新结果。
