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Phase Transitions and Orientational Order in a Two Dimensional Lennard-Jones System

  • Daan Frenkel
  • Frank E. Hanson
  • John P. McTague
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 50)

Abstract

It has long been suspected that the solid-fluid transition in two dimensions might be rather different than its 3-D counterpart, because of the lack of translational order in 2-D solids. Recently, a detailed theory of 2-D melting has been put forward by Halperin and Nelson.1 This theory provides a picture of 2-D melting that is indeed very different from what is observed in the three dimensional world. In particular, Halperin and Nelson (henceforth referred to as HN) make the intriguing prediction that, if 2-D melting is not a first order transition, then two second order transitions are required to go from the solid to the isotropic fluid phase. The solid and isotropic fluid phases will be separated by a peculiar liquid crystal-like phase which exhibits short range transiational order but long range “orientational” order.

Keywords

Triangular Lattice Orientational Order Melting Transition Orientational Order Parameter Isotropic Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    B. I. Halperin and D. R. Nelson, Phys. Rev. Lett., 41:121 (1978).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    J. P. McTague, M. Nielsen and L. Passell, CRC Critical Reviews in Solid State and Materials Sciences, 8:125 (1979) and references therein.ADSGoogle Scholar
  3. 3.
    T. T. Chung, unpublished, as quoted in ref. 4.Google Scholar
  4. 4.
    F. E. Hanson, M. J. Mandell and J. P. McTague, J. Phys. (PARIS), C-4:76 (1977).Google Scholar
  5. 5.
    M. J. Mandell, J. P. McTague and A. Rahman, J. Chem. Phys., 64:3699 (1976);ADSCrossRefGoogle Scholar
  6. 5a.
    M. J. Mandell, J. P. McTague and A. Rahman, J. Chem. Phys., 66:70 (1977).CrossRefGoogle Scholar
  7. 6.
    F. E. Hanson and J. P. McTague, to be published.Google Scholar
  8. 7.
    N. D. Mermin, Phys. Rev., 176:250 (1968).ADSCrossRefGoogle Scholar
  9. 8.
    R. M. Cctterill, E. J. Jensen and W. D. Kristensen, Spivn in: “Anharmonic Lattices, Structural Transitions and Melting,” Ed. T. Riste, Noordhoff, Leiden, 1974.Google Scholar
  10. 9.
    F. Tsien and J. P. Valleau, Mol. Phys., 27:177 (1974).ADSCrossRefGoogle Scholar
  11. 10.
    S. Toxvaerd, preprint.Google Scholar
  12. 11.
    D. Henderson, Mol. Phys., 34:1 (1977).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Daan Frenkel
    • 1
  • Frank E. Hanson
    • 1
  • John P. McTague
    • 1
  1. 1.Department of ChemistryUniversity of CaliforniaLos AngelesUSA

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