Skip to main content Accessibility help
×
Home

Heuristic Methods for Finding Ground-states of Ising Models

  • Hugues J. Lassalle (a1) and Luc T. Wille (a1)

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.

Copyright

References

Hide All
1. Kobe, S., J. Stat. Phys. 88, 991995 1997.
2. Zangwill, A., Physics at Surfaces, Cambridge University Press, Cambridge, 1988.
3. Ducastelle, F., Order and Phase Stability in Allows, North Holland, Amsterdam, 1991.
4. Baxter, R.J., Exactly Solved Models in Statistical Mechanics, Academic Press, New York, 1982.
5. Kanamori, J., Prog. Theor. Phys. 35, 1635 1966.
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. 117132.
7. Finel, A. and Ducastelle, F., in Phase Transformations in Solids, edited by Tsakalakos, T., (North Holland, Amsterdam, 1984) pp. 293298.
8. Ceder, G., Garbulsky, G.D., Avis, D., and Fukuda, F., Phys. Rev. B 49, 17 1994.
9. Horst, R. and Tuy, H., Global Optimization - Deterministic Approaches (Third ed.), Springer, Berlin, 1996.
10. Michalewicz, Z. and Fogel, D. B., How to Solve It: Modern Heuristics, Springer, Berlin, 2000.
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.
12. Kirkpatrick, S., Gellatt, C. D., and Vecchi, M.P., it Science 220, 671680 1983.
13. Wille, L. T., in Annual Reviews of Computational Physics, VII, edited by Stauffer, D., (World Scientific, Singapore, 2000) PP 2560.
14. Wales, D. J., this volume.

Heuristic Methods for Finding Ground-states of Ising Models

  • Hugues J. Lassalle (a1) and Luc T. Wille (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.