Abstract
The investigated application refers to simulations of exact groundstate energies and magnetizations of two-dimensional random Ising spin models on square as well as regular hexagonal and triangular L × L-lattices as considered in Solid State Physics when trying to determine for L→∞ the phase transition from ferro- to paramagnetism in magnetic crystal systems at zero temperature, cf. Bieche et al. (1980). In particular this requires to solve a quadratic integer programming problem, equivalent to a matching problem. The latter is efficiently solved by an exact algorithm based on works of Burkard, Derigs, Metz.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bendisch J, Derigs U, Metz A (1994) An efficient matching algorithm applied in Statistical Physics. Discrete Applied Mathematics
Bieche I, Maynard R, Rammal R, Uhry J (1980) On the groundstates of the frustration model of a spin glass. J. Phys A: Math Gen 13: 2553–2576
Burkard R, Derigs U (1980) Assignment and matching problems. Lecture Notes in Economics and Mathematical Systems 184. Springer-Verlag. Berl in NewYork
Derigs U (1981) A shortest augmenting path method for solving minimal perfect matching problems. Networks 11: 379–390
Derigs U (1986) Solving large-scale matching problems efficiently — A new primal approach Networks 16: 1–16
Derigs U, Metz A (1991) Solving large scale matching problems combinatorially. Mathematical Programming 50: 113–121
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Physica-Verlag Heidelberg
About this paper
Cite this paper
Bendisch, J., Derigs, U., Metz, A. (1994). Groundstates in Ising Spin Lattices by Optimal Matchings. In: Bachem, A., Derigs, U., Jünger, M., Schrader, R. (eds) Operations Research ’93. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-46955-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-46955-8_10
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-0794-3
Online ISBN: 978-3-642-46955-8
eBook Packages: Springer Book Archive