Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T06:54:28.591Z Has data issue: false hasContentIssue false
  • English
  • Français

Conventional and Unconventional Numerical Transfer-Matrix Methods

Published online by Cambridge University Press:  26 February 2011

M. A. Novotny  and
P. A. Rikvold
M. A. Novotny
Affiliation:
Supercomputer Computations Research Institute, B-186, Florida State University, Tallahassee, Florida 32306
P. A. Rikvold
Affiliation:
Physics Department and Center for Materials Research and Technology, B-159, Florida State University, Tallahassee, Florida 32306
Get access

Abstract

We briefly review the numerical transfer-matrix (TM) method and its application to materials science. We report on the conventional use of TM methods to calculate phase diagrams and critical exponents of classical statistical mechanical models in d=2. Examples presented here are spin-1/2 and spin-1 models (two- and three-state lattice-gas models). Discussed are a model for oxygen -ordering in the high temperature superconductor YBa2Cu3O6+x and a model for the electrosorption of an organic substance on a metal. Some results for the spin-1/2 model in d=3 are also presented. Three unconventional applications of the TM method will also be reported. These include a study of the surface tension of spin-1/2 models, a TM formalism for metastability, and a study of a translationally invariant (non-fractal) spin-1/2 model in non-integer dimensions.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 278: Symposium W – Computational Methods in Materials Science , 1992 , 15
Copyright
Copyright © Materials Research Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Binder, K., Monte Carlo Methods, (Springer-Verlag, Heidelberg, 1979).Google Scholar
[2] Nightingale, M. P. in Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by Privman, V., (World Scientific, Singapore, 1990), p. 287.Google Scholar
[3] Camp, W. J. and Fisher, M. E., Phys. Rev. B 6, 946 (1972).CrossRefGoogle Scholar
[4] Novotny, M. A., J. Math. Phys. 29, 2280 (1988).CrossRefGoogle Scholar
[5] Morgenstern, I. and Binder, K., Phys. Rev. Lett. 43, 1615 (1979).CrossRefGoogle Scholar
[6] Novotny, M. A., Europhys. Lett. 17, 297 (1992); 18, 92(E) (1992).CrossRefGoogle Scholar
[7] Aukrust, T. et al. , Phys. Rev. B 41 8772 (1990).CrossRefGoogle Scholar
[8] Wille, L. T., Berera, A., and Fontaine, D. de, Phys. Rev. Lett. 60, 1065 (1988).CrossRefGoogle Scholar
[9] Specht, E. D. et al. , Phys. Rev. B 37, 7426 (1988).CrossRefGoogle Scholar
[10] Bockris, J. O'M., Green, M., and Swinkels, D. A. J., J. Electrochem. Soc. 111, 736 (1964).CrossRefGoogle Scholar
[11] Rikvold, P. A. and Deakin, M. R., Surf. Sci. 294, 180 (1991).CrossRefGoogle Scholar
[12] Ferrenberg, A. M. and Landau, D. P., Phys. Rev. B 44, 5081 (1991).CrossRefGoogle Scholar
[13] Mon, K. K., Landau, D. P., and Stauffer, D., Phys. Rev. B 42, 545 (1990).CrossRefGoogle Scholar
[14] Privman, V. and Švrakić, N. M., Phys. Rev. Lett. 62, 633 (1989).CrossRefGoogle Scholar
[15] Novotny, M. A., Richards, H. L., and Rikvold, P. A. in Interface Dynamics and Growth, (Mater. Res. Soc. Symp. Proc. 237), in press.Google Scholar
[16] Novotny, M. A., unpublished.Google Scholar
[17] Harris, A. B., J. Phys. C 7, 1671 (1974).CrossRefGoogle Scholar
[18] Guillou, J. C. Le and Zinn-Justin, J., J. Physique 48, 19 (1987).CrossRefGoogle Scholar
[19] Wallace, D. J. and Zia, R. K. P., Phys. Rev. Lett. 43, 808 (1979).CrossRefGoogle Scholar
[20] Forster, D. and Gabriunas, A., Phys. Rev. A 24, 598 (1981).CrossRefGoogle Scholar
[21] Fisch, R., J. Stat. Phys. 18, 111 (1978).CrossRefGoogle Scholar
[22] Rikvold, P. A., Gorman, B. M., and Novotny, M. A., Am. Inst. Phys. Conf. Proc. Series, Slow Dynamics in Condensed Matter, in press.Google Scholar
[23] Novotny, M. A., Klein, W., and Rikvold, P. A., Phys. Rev. B 33, 7729 (1986).CrossRefGoogle Scholar