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Microscopic approach to calculation of the shear and bulk moduli and the frank constant in two-dimensional melting

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Abstract

Microscopic expressions are obtained for the shear and bulk moduli in the vicinity of the melting line and for the Frank constant of the hexatic phase in terms of the potential, the radial distribution function, and the direct correlation function.

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References

  1. B. I. Halperin and D. R. Nelson,Phys. Rev. Lett.,41, 121 (1978).

    Google Scholar 

  2. A. P. Young,Phys. Rev. B.,19, 1855 (1979).

    Google Scholar 

  3. D. R. Nelson and B. I. Halperin,Phys. Rev. B,19, 2457 (1979).

    Google Scholar 

  4. D. R. Nelson,Phys. Rev. B,26, 269 (1982).

    Google Scholar 

  5. J. M. Kosterlitz and D. J. Thouless,J. Phys. C,6, 1181 (1974).

    Google Scholar 

  6. A. Z. Patashinskii and V. L. Pokrovskii,Fluctuation Theory of Phase Transitions [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  7. K. J. Stanburg,Rev. Mod. Phys.,60, 161 (1988).

    Google Scholar 

  8. D. R. Nelson and J. Toner,Phys. Rev. B,24, 363 (1981).

    Google Scholar 

  9. V. N. Ryzhov,Teor. Mat. Fiz.,88, 449 (1991).

    Google Scholar 

  10. V. N. Ryzhov,Zh. Eksp. Teor. Fiz.,100, 1627 (1991).

    Google Scholar 

  11. G. Leibfried, “Gittertheorie der mechanischen und thermischen Eigenschaften der Kristalle,” in:Handbuch der Physik (ed. J. Flügge), Vol. 7 Part 1, Springer Verlag, Berlin (1955), pp. 104–324.

    Google Scholar 

  12. V. N. Ryzhov and E. E. Tareyeva,Phys. Lett. A,158, 321 (1991).

    Google Scholar 

  13. N. N. Bogolyubov, “Problems of a dynamical theory in statistical physics,” in:Studies, in Statistical Mechanics, Vol. 1 (eds. J. de Boer and G. E. Uhlenbeck), North-Holland, Amsterdam (1962).

    Google Scholar 

  14. V. N. Ryzhov and E. E. Tareeva,Teor. Mat. Fiz.,73, 463 (1987).

    Google Scholar 

  15. V. N. Ryzhov,J. Phys.,2, 5855 (1990).

    Google Scholar 

  16. L. D. Landau and E. M. Lifshitz,Theory of Elasticity, 2nd ed., Pergamon Press, Oxford (1970).

    Google Scholar 

  17. L. D. Landau and E. M. Lifshitz,Statistical Physics, Part. 1 [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  18. N. D. Mermin,Phys. Rev.,176, 250 (1968).

    Google Scholar 

  19. V. N. RyzhovTeor. Mat. Fiz.,55, 128 (1983).

    Google Scholar 

  20. R. Balescu,Equilibrium and Nonequilibrium Statistical Mechanics, Wiley-Interscience New York (1975).

    Google Scholar 

  21. N. N. Bogolyubov, “Quasiaverages in problems of statistical mechanics,” Preprint JINR 788 [in Russian], JINR, Dubna (1961).

    Google Scholar 

  22. V. N. Ryzhov,Teor. Mat. Fiz.,80, 107 (1989).

    Google Scholar 

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Authors
  1. V. N. Ryzhov
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  2. E. E. Tareeva
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Additional information

L. F. Vereshchagin Institute of High Pressures, Russian Academy of Sciences Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 2, pp. 331–343, August, 1992.

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Ryzhov, V.N., Tareeva, E.E. Microscopic approach to calculation of the shear and bulk moduli and the frank constant in two-dimensional melting. Theor Math Phys 92, 922–930 (1992). https://doi.org/10.1007/BF01015558

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  • DOI: https://doi.org/10.1007/BF01015558

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