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Numerical Transfer-Matrix Study Of Interfaces In Ising Models

Published online by Cambridge University Press:  21 February 2011

M. A. Novotny
Affiliation:
Supercomputer Computations Research Institute, B-186, Florida State University, Tallahassee, Florida 32306
H. L. Richards
Affiliation:
Supercomputer Computations Research Institute, B-186, Florida State University, Tallahassee, Florida 32306 Physics Department and Center for Materials Research and Technology, B-159, Florida State University, Tallahassee, Florida 32306
P. A. Rikvold
Affiliation:
Supercomputer Computations Research Institute, B-186, Florida State University, Tallahassee, Florida 32306 Physics Department and Center for Materials Research and Technology, B-159, Florida State University, Tallahassee, Florida 32306 Tohwa Institute for Science, Tohwa University, Fukuoka 815, Japan Department of Physics, Kyushu University, 33, Fukuoka 812, Japan
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Abstract

Results are reported for the surface tension, the surface free energy, the surface stiffness coefficient, and the single-step free energy for the Ising model in two and three dimensions. These are obtained by numerical transfer-matrix calculations, testing detailed predictions for the scaling of the largest eigenvalues of the transfer-matrix.

Type
Research Article
Copyright
Copyright © Materials Research Society 1992

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References

[1] For reviews see Binder, K. in Phase Transitions and Critical Phenomena, Vol. 8, ed. Domb, C. and Lebowitz, J. L. (Academic, New York, 1983);Google Scholar
Gelfand, M. P. and Fisher, M. E., Physica A 166, 1 (1990);CrossRefGoogle Scholar
Jasnow, D. in Phase Transitions and Critical Phenomena, Vol. 10, ed. Domb, C. and Lebowitz, J. L. (Academic, New York, 1986).Google Scholar
[2] Shaw, L. J. and Fisher, M. E., Phys. Rev. A 39, 2189 (1989).Google Scholar
[3] Mon, K. K., Wansleben, S., Landau, D. P., and Binder, K., Phys. Rev. Lett. 60, 708 (1988)CrossRefGoogle Scholar
[4] Mon, K. K., Wansleben, S., Landau, D. P., and Binder, K., Phys. Rev. B 39, 7089 (1989).Google Scholar
[5] Mon, K.K., Landau, D. P., and Stauffer, D., Phys. Rev. B 42, 545 (1990).Google Scholar
[6] Meyer-Ortmanns, H. and Trappenberg, T., J. Stat. Phys. 58, 185 (1990).Google Scholar
[7] Münster, G., Nucl. Phys. 324, 630 (1989).CrossRefGoogle Scholar
[8] Ueno, Y., Sun, G., and Ono, I., J. Phys. Soc. Jap. 58, 1162 (1989).CrossRefGoogle Scholar
[9] Sun, G. and Ueno, Y., Z. Phys. B 82, 425 (1991).CrossRefGoogle Scholar
[10] Privman, V. and Švrakić, N. M., Phys. Rev. Lett. 62, 633 (1989).CrossRefGoogle Scholar
[11] Privman, V. and Švrakić, N. M, J. Stat. Phys. 54, 735 (1989).Google Scholar
[12] Abraham, D. B. L. F., Ko, and Švrakić, N. M., J. Stat. Phys. 56, 563 (1989).Google Scholar
[13] Abraham, D. B., Švrakić, N. M., and Upton, P. J., preprint HLRZ 69/91.Google Scholar
[14] Selke, W., Švrakić, N. M., and Upton, P. J., preprint HLRZ 64/91.Google Scholar
[15] Fisher, M. P. A., Fisher, D. S., and Weeks, J. D., Phys. Rev. Lett. 48, 368 (1982).Google Scholar
[16] Kramers, H. A. and Montroll, G. H., Phys. Rev. 60, 252 (1941).CrossRefGoogle Scholar
[17] Camp, W. J. and Fisher, M. E., Phys. Rev. 6, 946 (1972).Google Scholar
[18] Statistical Mechanics, Huang, K., p. 352, (Wiley, New York, 1963).Google Scholar
[19] Novotný, M. A., J. Math. Phys. 29, 2280 (1988).Google Scholar
[20] Nightingale, M. P. in Finite Size Scaling and Numerical Simulation of Statistical Systems, ed. Privman, V., (World Scientific, Singapore, 1990).Google Scholar
[21] Novotný, M. A., Richards, H. L., and Rikvold, P. A., unpublished.Google Scholar
[22] Abraham, D. B., Gallavotti, G., and Martin-Löff, A., Physica 65, 73 (1973).Google Scholar
[23] Fisher, M. E. and Ferdinand, A. E., Phys. Rev. Lett. 19, 169 (1967).Google Scholar
[24] Ferrenberg, A. M. and Landau, D. P., Phys. Rev. 44, 5081 (1991).Google Scholar