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Heuristic Methods for Finding Ground-states of Ising Models

Published online by Cambridge University Press:  17 March 2011

Hugues J. Lassalle  and
Luc T. Wille
Hugues J. Lassalle
Affiliation:
Florida Atlantic University, Physics Department, Boca Raton, FL 33431, U.S.A.
Luc T. Wille
Affiliation:
Florida Atlantic University, Physics Department, Boca Raton, FL 33431, U.S.A.
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Abstract

We describe rhe application of simulated annealing and genetic algorithms to determine the ground-state of various classes of Lsing models. This problem is relevant to finding equilibrium contigurations(at zero Kelvin)of adsorbed monolayers, multi-component alloys, and magnetic systems. Because of the presence of metastable configurations (local minima) the detection of the ground-state (global minimum) is a non-trivial problem, especially in the case of complex interactions or frustrated systems. The speed of convergends analyzed for various model systems.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 700: Symposium S – Combinatorial and Artificial Intelligence Methods in Materials Science , 2001 , S8.7
Copyright
Copyright © Materials Research Society 2002

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References

1. Kobe, S., J. Stat. Phys. 88, 991–995 1997.Google Scholar
2. Zangwill, A., Physics at Surfaces, Cambridge University Press, Cambridge, 1988.Google Scholar
3. Ducastelle, F., Order and Phase Stability in Allows, North Holland, Amsterdam, 1991.Google Scholar
4. Baxter, R.J., Exactly Solved Models in Statistical Mechanics, Academic Press, New York, 1982.Google Scholar
5. Kanamori, J., Prog. Theor. Phys. 35, 16–35 1966.Google Scholar
6. Sanchez, J.M. and Fontaine, D. de, in Structure and Bonding in Crystals, Vol. II, edited by O'Keeffe, M. and Navrotsky, A., (Academic Press, New York, 1981) pp. 117–132.Google Scholar
7. Finel, A. and Ducastelle, F., in Phase Transformations in Solids, edited by Tsakalakos, T., (North Holland, Amsterdam, 1984) pp. 293–298.Google Scholar
8. Ceder, G., Garbulsky, G.D., Avis, D., and Fukuda, F., Phys. Rev. B 49, 1–7 1994.Google Scholar
9. Horst, R. and Tuy, H., Global Optimization - Deterministic Approaches (Third ed.), Springer, Berlin, 1996.Google Scholar
10. Michalewicz, Z. and Fogel, D. B., How to Solve It: Modern Heuristics, Springer, Berlin, 2000.Google Scholar
11. Lassalle, H. J. and Wille, L. T., in Priceedings of the Third International Conference on Intelligent Processing and Manufacturing of Magurials, edited by Meech, J. A., Veiga, S. M., Veiga, M. M., LeClair, S. R. and Maguire, J.F., eds., (IPMM, Vancouver, 2001), CD-ROM.Google Scholar
12. Kirkpatrick, S., Gellatt, C. D., and Vecchi, M.P., it Science 220, 671–680 1983.Google Scholar
13. Wille, L. T., in Annual Reviews of Computational Physics, VII, edited by Stauffer, D., (World Scientific, Singapore, 2000) PP 25–60.Google Scholar
14. Wales, D. J., this volume.Google Scholar