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Models of defect-mediated melting

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Abstract

A survey is given of recent Monte Carlo studies of lattice defect models for melting in three and two dimensions. In two dimensions special emphasis is laid upon a recently proposed model which exhibits a crossover from a single first-order transition to two successive transitions of the Kosterlitz-Thouless type.

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References

  • Ami, S., and Kleinert, H. (1984).Journal de Physique,45, L877.

    Google Scholar 

  • Banks, T., Myerson, R., and Kogut, J. (1977).Nuclear Physics B,129, 493.

    Google Scholar 

  • Berezinskii, V. L. (1970).Zhurnal Eksperimental'noi i Teoreticheskoi Fizika,59, 907 [Soviet Physics—JETP 32, 493 (1971)].

    Google Scholar 

  • Berezinskii, V. L. (1971).Zhurnal Eksperimental'noi i Teoreticheskoi Fizika,61, 1144 [Soviet Physics—JETP 34, 610 (1972)].

    Google Scholar 

  • Bowers, R. G., and Joyce, G. S. (1967).Physical Review Letters,19, 630.

    Google Scholar 

  • Bruce, D. A. (1985).Materials Science Forum,4, 51.

    Google Scholar 

  • Burton, J. A., Cabrera, N., and Frank, F. C. (1951).Philosophical Transactions of the Royal Society of London A,243, 299.

    Google Scholar 

  • Byckling, E. (1965).Annals of Physics,32, 367.

    Google Scholar 

  • Chui, S. T. (1982).Physical Review Letters,48, 933.

    Google Scholar 

  • Chui, S. T. (1983).Physical Review B,28, 178.

    Google Scholar 

  • Dasgupta, C., and Halperin, B. I. (1981).Physical Review Letters,47, 1556.

    Google Scholar 

  • Feynman, R. P. (1955). InProgress in Low Temperature Physics, Vol. 1, C. J. Gorter, ed., North-Holland, Amsterdam, p. 17.

    Google Scholar 

  • Gay, J. M., Suzanne, J., Pepe, G., and Meichel, T. (1988).Surface Science,204, 69.

    Google Scholar 

  • Gupte, N., and Shenoy, S. R. (1986).Physical Review D,33, 3002.

    Google Scholar 

  • Halperin, B. I., and Nelson, D. R. (1978).Physical Review Letters,41, 121 [Erratum,41, 519(E) (1978)].

    Google Scholar 

  • Helfrich, W. (1978).Journal de Physique,39, 1199.

    Google Scholar 

  • Jacobs, L., and Kleinert, H. (1984).Journal of Physics A,17, L361.

    Google Scholar 

  • Janke, W. (1985). Ph.D. thesis, FU Berlin (unpublished).

  • Janke, W., and Kleinert, H. (1984).Physics Letters,105A, 143.

    Google Scholar 

  • Janke, W., and Kleinert, H. (1985). Unpublished results.

  • Janke, W., and Kleinert, H. (1986a).Nuclear Physics B,270[FS 16], 135.

    Google Scholar 

  • Janke, W., and Kleinert, H. (1986b).Physical Review B,33, 6346.

    Google Scholar 

  • Janke, W., and Kleinert, H. (1986c).Physics Letters,114A, 255.

    Google Scholar 

  • Janke, W., and Kleinert, H. (1988).Physical Review Letters,61, 2344 [Erratum,62, 608(E) (1989)].

    Google Scholar 

  • Janke, W., and Kleinert, H. (1989).Physics Letters,140A, 513.

    Google Scholar 

  • Janke, W., and Kleinert, H. (1990).Physical Review B,41, 6848.

    Google Scholar 

  • Janke, W., and Toussaint, D. (1986).Physics Letters,116A, 387.

    Google Scholar 

  • Kapitza, P. L. (1937).Nature 141, 74.

    Google Scholar 

  • Kapitza, P. L. (1941).Journal of Experimental and Theoretical Physics (USSR),11, 1.

    Google Scholar 

  • Kleinert, H. (1982a).Lettere Nuovo Cimento,34, 103.

    Google Scholar 

  • Kleinert, H. (1982b).Lettere Nuovo Cimento,34, 464.

    Google Scholar 

  • Kleinert, H. (1982c).Physics Letters,91A, 295.

    Google Scholar 

  • Kleinert, H. (1982d).Physics Letters,93A, 86.

    Google Scholar 

  • Kleinert, H. (1983a).Journal of Physics (Paris),44, 353.

    Google Scholar 

  • Kleinert, H. (1983b).Physics Letters,95A, 381.

    Google Scholar 

  • Kleinert, H. (1983c).Physics Letters,95A, 493.

    Google Scholar 

  • Kleinert, H. (1983d).Lettere Nuovo Cimento,37, 295.

    Google Scholar 

  • Kleinert, H. (1983e).Physics Letters,96A, 302.

    Google Scholar 

  • Kleinert, H. (1983f).Physics Letters,97A, 51.

    Google Scholar 

  • Kleinert, H. (1988a).Physics Letters,130A, 59.

    Google Scholar 

  • Kleinert, H. (1988b).Physics Letters,130A, 443.

    Google Scholar 

  • Kleinert, H. (1989a).Gauge Fields in Condensed Matter, World Scientific, Singapore.

    Google Scholar 

  • Kleinert, H. (1989b).Physics Letters,136A, 468.

    Google Scholar 

  • Kosterlitz, J. M. (1974).Journal of Physics C,7, 1046.

    Google Scholar 

  • Kosterlitz, J. M., and Thouless, D. J. (1973).Journal of Physics C,6, 1181.

    Google Scholar 

  • Kosterlitz, J. M., and Thouless, D. J. (1978).Progress in Low Temperature Physics,7B, 371.

    Google Scholar 

  • Larese, J. Z., Passell, L., Heidemann, A. D., Richter, D., and Wicksted, J. P. (1988).Physical Review Letters,61, 432.

    Google Scholar 

  • Lipa, J. A., and Chui, T. C. P. (1983).Physical Review Letters,51, 2291.

    Google Scholar 

  • Lund, F., Reisenegger, A., and Utreras, C. (1990).Physical Review B,41, 155.

    Google Scholar 

  • Minnhagen, P. (1987).Review of Modern Physics,59, 1001.

    Google Scholar 

  • Mueller, K. H., Ahlers, G., and Pobell, F. (1976).Physical Review B,14, 2096.

    Google Scholar 

  • Nelson, D. R. (1979).Physical Review B,18, 2318.

    Google Scholar 

  • Nelson, D. R. (1982).Physical Review B,26, 269.

    Google Scholar 

  • Nelson, D. R., and Halperin, B. I. (1979).Physical Review B,19, 2457.

    Google Scholar 

  • Nelson, D. R., and Toner, J. (1981).Physical Review B,24, 363.

    Google Scholar 

  • Nham, H. S., and Hess, G. B. (1988).Physical Review B,38, 5166.

    Google Scholar 

  • Onsager, L. (1949).Nuovo Cimento Supplemento,6, 249.

    Google Scholar 

  • Popov, V. N. (1973).Zhurnal Eksperimental'noi i Teoreticheskoi Fizika 64, 672 [Soviet Physics—JETP 37, 341 (1973)].

    Google Scholar 

  • Savit, R. (1980).Review of Modern Physics,52, 453.

    Google Scholar 

  • Shenoy, S. R. (1989).Physical Review B,40, 5056.

    Google Scholar 

  • Shockley, W. (1952). InL'Etat Solide (Proceedings of Neuvienne-Consail de Physique, Brussels), R. Stoops, ed., Institut de Physique, Solvay, Brussels.

    Google Scholar 

  • Shugard, W. J., Weeks, J. D., and Gilmer, G. H. (1978).Physical Review Letters,41, 1399 [Erratum,41, 1577(E) (1978)].

    Google Scholar 

  • Strandburg, K. J. (1986).Physical Review B,34, 3536.

    Google Scholar 

  • Strandburg, K. J. (1988).Review of Modern Physics,60, 161 (1988) [Erratum,61,747(E) (1989)].

    Google Scholar 

  • Strandburg, K. J., Solla, S. A., and Chester, G. V. (1983).Physical Review B,28, 2717.

    Google Scholar 

  • Taub, H. (1988). InThe Time Domain in Surface and Structural Dynamics, G. J. Long and F. Grandjean, eds., Kluwer, Dordrecht, p. 467.

    Google Scholar 

  • Ubbelohde, A. R. (1978).The Molten State of Matter, Wiley, New York.

    Google Scholar 

  • Vaks, V. G., and Larkin, A. I. (1965).Zhurnal Eksperimental'noi i Teoreticheskoi Fizika,49, 975 [Soviet Physics—JETP,22, 678 (1966)].

    Google Scholar 

  • Villain, J. (1975).Journal de Physique,36, 581.

    Google Scholar 

  • Wensley, R. J., and Stack, J. D. (1989).Physical Review Letters,63, 1764.

    Google Scholar 

  • Wiegel, F. W. (1973).Physica,65, 321.

    Google Scholar 

  • Wiegel, F. W. (1975).Physics Reports,16, 58.

    Google Scholar 

  • Wiegel, F. W. (1986).Introduction to Path Integral Methods in Physics and Polymer Science, World Scientific, Singapore.

    Google Scholar 

  • Williams, G. A. (1987).Physical Review Letters,59, 1926 [Erratum,61, 1142(E) (1988)].

    Google Scholar 

  • Young, A. P. (1979).Physical Review B,19, 1855.

    Google Scholar 

  • Zhang, S., and Migone, A. D. (1988).Physical Review B,38, 12039.

    Google Scholar 

  • Zhang, S., and Migone, A. D. (1989).Surface Science,222, 31.

    Google Scholar 

Download references

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Janke, W. Models of defect-mediated melting. Int J Theor Phys 29, 1251–1270 (1990). https://doi.org/10.1007/BF00672935

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