Details
| Original language | English |
|---|---|
| Article number | 193 |
| Journal | Entropy |
| Volume | 21 |
| Issue number | 2 |
| Early online date | 18 Feb 2019 |
| Publication status | Published - Feb 2019 |
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 du = 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.
Keywords
- Disordered systems, Frustration, Negative weight percolation, Optimisation, Phase transition
ASJC Scopus subject areas
- Computer Science(all)
- Information Systems
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
- Engineering(all)
- Electrical and Electronic Engineering
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In: Entropy, Vol. 21, No. 2, 193, 02.2019.
Research output: Contribution to journal › Review article › Research › peer review
}
TY - JOUR
T1 - From Spin Glasses to Negative-Weight Percolation
AU - Hartmann, Alexander K.
AU - Melchert, Oliver
AU - Norrenbrock, Christoph
N1 - Funding Information: Financial support is announced from the DFG (Deutsche Forschungsgemeinschaft) under grantHA3169/3-1 and within the Graduiertenkolleg 1885 "Molecular Basis of Sensor Biology". The simulations were performed at the HPC Clusters HERO and CARL, located at the University of Oldenburg (Germany) and funded by the DFG through its Major Instrumentation Programme (INST 184/108-1 FUGG and INST 184/157-1 FUGG) and the Ministry of Science and Culture (MWK) of the Lower Saxony State.
PY - 2019/2
Y1 - 2019/2
N2 - 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 du = 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.
AB - 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 du = 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.
KW - Disordered systems
KW - Frustration
KW - Negative weight percolation
KW - Optimisation
KW - Phase transition
UR - http://www.scopus.com/inward/record.url?scp=85061990224&partnerID=8YFLogxK
U2 - 10.3390/e21020193
DO - 10.3390/e21020193
M3 - Review article
AN - SCOPUS:85061990224
VL - 21
JO - Entropy
JF - Entropy
SN - 1099-4300
IS - 2
M1 - 193
ER -