Exact ground states of large two-dimensional planar Ising spin glasses

Pardella GL, Liers F (2008)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2008

Journal

Physical Review E American Physical Society

Publisher: American Physical Society

Book Volume: 78

Article Number: 056705

Journal Issue: 5

DOI: 10.1103/PhysRevE.78.056705

Abstract

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-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to 30002 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. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the L. Bieche approach. © 2008 The American Physical Society.

Authors with CRIS profile

Frauke Liers-Bergmann Professur für Optimization under Uncertainty & Data Analysis

Involved external institutions

Universität zu Köln DE Germany (DE)

How to cite

APA:

Pardella, G.L., & Liers, F. (2008). Exact ground states of large two-dimensional planar Ising spin glasses. Physical Review E, 78(5). https://dx.doi.org/10.1103/PhysRevE.78.056705

MLA:

Pardella, Gregor L., and Frauke Liers. "Exact ground states of large two-dimensional planar Ising spin glasses." Physical Review E 78.5 (2008).

BibTeX: Download