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Pardella, Gregor and Liers, Frauke (2008). Exact Ground States of Large Two-Dimensional Planar Ising Spin Glasses. Physical Review E, 78 (5). 056705. American Physical Society.

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Abstract

We present an algorithm for the calculation of exact ground states of two-dimensional Ising spin glasses with free boundary conditions in at least one direction. Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum weighted perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and memory requirements. Using Kasteleyn cities, we calculate accurate ground states for huge two-dimensional planar Ising spin-glass lattices (up to 3000x3000 spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Domain walls can be computed using reoptimization. Finally, the correctness of heuristically computed ground states can easily be verified.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Pardella, Gregor UNSPECIFIED UNSPECIFIED UNSPECIFIED Liers, Frauke UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-549263
Journal or Publication Title:	Physical Review E
Volume:	78
Number:	5
Page Range:	056705
Date:	2008
Publisher:	American Physical Society
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Institute of Computer Science
Subjects:	Data processing Computer science
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/54926