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Prog. Theor. Phys. Vol. 61 No. 6 (1979) pp. 1584-1596

[ Full Text PDF : FREE ACCESS (959K) ]

A Simple Theory of Hard Disk Transition

Hikaru Kawamura

Department of Physics, University of Tokyo, Tokyo 113

(Received January 11, 1979)

Abstract:

The solid-fluid phase transition of a two-dimensional hard disk system is studied by using a simple model proposed by Collins. This is a simplified Bernal lattice consisting of closed-packed equilateral triangles and squares. It is important to take account of a geometrical constraint by a short range correlation in calculating the entropy. We find the phase transition at PA0/NkBT ≃ 6.90, (A/A0)s ≃ 1.273 and (A/A0)f ≃ 1.345, where A is the total area of the system and A0 is the area at the close-packing by the triangles. The subscripts s and f denote the solid and fluid phases respectively. The corresponding values by computer experiments were PA0/NkBT ≃ 7.72, (A/A0)s ≃ 1.266 and (A/A0)f ≃ 1.312. The equation of state and specific heat at constant pressure are calculated. The primary origin of the hard disk transition and melting is attributed to the intrinsic disorder of the fluid phase.


URL : http://ptp.ipap.jp/link?PTP/61/1584/
DOI : 10.1143/PTP.61.1584

[ Full Text PDF : FREE ACCESS (959K) ] Citation:

References:

  1. W. W. Wood and J. D. Jacobson, J. Chem. Phys. 27 (1957), 1207[CrossRef].
  2. W. W. Wood, Physics of Simple Liquids, edited by H. N. V. Temperley, J. S. Rowlinson and G. S. Rushbrooke (North-Holland, Amsterdam, 1968), p. 115.
  3. B. J. Alder and T. E. Wainwright, J. Chem. Phys. 27 (1957), 1208[CrossRef]; ibid. 33 (1960), 1439[CrossRef].
  4. B. J. Alder and W. G. Hoover, Physics of Simple Liquids, edited by H. N. V. Temperley, J. S. Rowlinson and G. S. Rushbrooke (North-Holland, Amsterdam, 1968), p. 79.
  5. W. G. Hoover and F. H. Ree, J. Chem. Phys. 49 (1968), 3609[CrossRef]; ibid. 47 (1967), 4873[CrossRef].
  6. B. J. Alder and T. E. Wainwright, Phys. Rev. 127 (1962), 359[APS].
  7. H. C. Longuet-Higgins and B. Widom, Mol. Phys. 8 (1964), 549.
  8. J. A. Barker and D. Henderson, J. Chem. Phys. 47 (1967), 2856[CrossRef]; ibid. 47 (1967), 4714[CrossRef].
  9. H. C. Anderson, D. Chandler and J. D. Weeks, J. Chem. Phys. 56 (1972), 3812[CrossRef].
  10. J. D. Bernal, Proc. R. Soc. A 280 (1964), 299.
    J. D. Bernal and S. V. King, Physics of Simple Liquids (see Ref. 2)), p. 231.
  11. R. Collins, Phase Transition and Critical Phenomena, edited by C. Domb and M. S. Green (Academic Press, New York, 1972), vol. 2, p. 271.
  12. J. L. Finey, Proc. R. Soc. A 319 (1970), 479; ibid. 319 (1970), 495.
  13. T. Ogawa and M. Tanemura, Prog. Theor. Phys. 51 (1974), 399[PTP].
  14. J. E. Lennard-Jones and A. F. Devonshire, Proc. R. Soc. A 169 (1939), 317; ibid. 170 (1939), 464.
  15. L. K. Runnels, Phase Transition and Critical Phenomena vol. 2, (see Ref. 11)), p. 305.
  16. B. J. Alder, W. G. Hoover and T. E. Wainwright, Phys. Rev. Lett. 11 (1963), 241[APS].
  17. H. Mori, H. Okamoto and S. Isa, Prog. Theor. Phys. 47 (1972), 1087[PTP].
    H. Okamoto, S. Isa and H. Mori, Prog. Theor. Phys. 48 (1972), 731[PTP].
    H. Mori, S. Isa, H. Okamoto and H. Furukawa, Prog. Theor. Phys. 48 (1972), 1474[PTP].
    H. Okamoto, S. Isa, N. Hijikuro and H. Mori, Prog. Theor. Phys. 50 (1973), 1248[PTP].
  18. T. Ichimura, T. Shiotani and A. Ueda, Prog. Theor. Phys. 60 (1978), 941[PTP].
  19. R. Collins, Proc. Phys. Soc. 83 (1964), 553.
  20. A. Eisenstein and N. S. Gingrich, Phys. Rev. 62 (1942), 261[APS].
    D. G. Henshaw, Phys. Rev. 105 (1957), 976[APS].
    G. T. Clayton and L. Heaton, Phys. Rev. 121 (1961), 649[APS].
    K. Furukawa, Rep. Prog. Theor. Phys. 25 (1962), 395[PTP].
  21. J. E. Lenard-Jones and A. F. Devonshire, Proc. R. Soc. A 163 (1937), 63; ibid. 165 (1938), 1.
  22. L. G. Caron, J. Chem. Phys. 55 (1971), 5227[CrossRef].
  23. T. Ichimura, N. Ogita and A. Ueda, J. Phys. Soc. Jpn. 45 (1978), 252[JPSJ].
  24. W. W. Wood, J. Chem. Phys. 20 (1952), 1334[AIP Scitation].
  25. F. A. Lindemann, Z. Phys. 11 (1910), 609.
  26. M. Ross, Phys. Rev. 184 (1969), 233[APS].
  27. J. N. Shapiro, Phys. Rev. B 1 (1970), 3982[APS].
  28. N. D. Mermin, Phys. Rev. 176 (1968), 250[APS].
    J. F. Fernandez, Phys. Rev. B 1 (1970), 1345[APS].

Citing Article(s) :

  1. ERROR : Mag:19, Vol:439, Page:
  2. Progress of Theoretical Physics Vol. 63 No. 1 (1980) pp. 24-41 :
    A Simple Theory of Melting and Condensation in Two-Dimensional System
    Hikaru Kawamura
  3. Progress of Theoretical Physics Vol. 64 No. 2 (1980) pp. 419-435 :
    Lattice Model of Quantum Melting
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  4. Progress of Theoretical Physics Vol. 70 No. 2 (1983) pp. 352-365 :
    Statistics of Two-Dimensional Amorphous Lattice
    Hikaru Kawamura
  5. Progress of Theoretical Physics Vol. 70 No. 3 (1983) pp. 687-696 :
    Hole Model Approach to Melting
    Shigeru Shinomoto
  6. Progress of Theoretical Physics Vol. 70 No. 5 (1983) pp. 1197-1206 :
    A Simplified Model of Phase Transition in Amorphous Antiferromagnets. II
    Hikaru Kawamura
  7. Progress of Theoretical Physics Vol. 73 No. 2 (1985) pp. 311-318 :
    A Simplified Model of Phase Transition in Amorphous Antiferromagnets. III
    Hikaru Kawamura
  8. Progress of Theoretical Physics Vol. 78 No. 1 (1987) pp. 83-96 :
    Information Entropy and the Statistical Geometry of Two-Dimensional Liquids
    Robert Collins, Tohru Ogawa and Taeko Ogawa
  9. Progress of Theoretical Physics Supplement No. 178 (2009) pp. 41-48 :
    Non-Equilibrium Relaxation Analysis on Two-Dimensional Melting
    Hiroshi Watanabe

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