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System of hard squares in two dimensions (2D) has been studied by Monte Carlo simulations. The simulations indicate that the isotropic fluid phase in this system does not freeze into a 2D 'crystal-line' phase (of square lattice and quasi-long-range translational order) but transforms into an inter-mediate phase with the quadratic quasi-long-range orientational order (of coupled molecular axes and intermolecular bonds) and the translational order decaying faster than algebraically. The equation of state and the specific heat of the system are surprisingly well reproduced by smoothed version of the free volume theory in the whole density range.
Rocznik
Tom
Strony
235--255
Opis fizyczny
Bibliogr. 41 poz., rys., wykr.
Twórcy
autor
- Institute of Molecular Physics, Polish Academy of Sciences Smoluchowskiego 17/19, 60-179 Poznań, Poland
autor
- FOM - Institute for Atomic and Molecular Physics Postbus 41883, 1009 DB Amsterdam, The Netherlands
Bibliografia
- [1] B. J. Alder and W. G. Hoover, in Physics of Simple Liquids, Ed. H. N. V. Temperley, J. S. Rowlinson, and G. S. Rushbrooke, (North-Holland, 1968).
- [2] J. Vieillard-Baron, J. Chem. Phys. 56, 4729 (1972).
- [3] D. Frenkel and B. Mulder, Molec. Phvs. 55, 1171 (1985).
- [4] A. Stroobants, H. N. W. Lekkerkerker, and D. Frenkel, Phvs. Rev. Lett. 57, 1452 (1987); Phvs. Rev. A 36, 2929(1987).
- [5] K. W. Wojciechowski, A. C. Brańka, and M. Parrinello, Molec. Phvs. 53, 1541 (1984).
- [6] A. C. Brańka and K. W. Wojciechowski, Molec. Phys. 72, 941 (1991); ibid. 78, 1513 (1993).
- [7] D. Frenkel, in: Liquids, Freezing and Glass Transition, Les Houches LI, Eds. J. P. Hansen, D. Levesque and J. Zinn-Justin, Elsevier (1991).
- [8] J. A. C. Veerman and D. Frenkel, Phys. Rev. A 45, 5632 (1992).
- [9] K. W. Wojciechowski, D. Frenkel, and A. C. Brańka, Phvs. Rev. Lett. 66, 3168 (1991); Phvsica A 196, 519-545 (1993).
- [10] K. W. Wojciechowski, Phys. Rev. B 46, 26 (1992).
- [11] L. Onsager, Phys. Rev. 62, 558 (1942); L. Onsager, Ann. NY Acad. Sci. 51, 3441 (1949).
- [12] K. W. Wojciechowski and J. Kłos, Nematic phase of cubic symmetiy: Solution of the Frenkel 3D-cross model, unpublished.
- [13] R. Schneider, Convex bodies: The Brunn-Minkowski Theoiy Vol. 44 of Encyclopedia of Mathematics and its Applications, Ed. G.-C. Rota (Cambridge, 1993).
- [14] T. Boublik, Mol. Phys. 29, 421 (1975).
- [15] G. Tarjus, P. Viot, S. M. Ricci, and J. Talbot, Mol. Phys. 73, 773 (1991).
- [16] K. W. Wojciechowski and D. Frenkel, On the phase diagram of two-dimensional hard rectangle system, unpublished.
- [17] J. A. Zollweg and G. V. Chester, Phys. Rev B 46, 11186 (1992).
- [18] J. Lee and K. J. Strandburg, Phvs. Rev. B 17, 11190 (1992).
- [19] R. E. Peierls, Helv. Phys. Acta 7, 81 (1934).
- [20] L. D. Landau and E. M. Lifshitz, Statistical Physics, Part I (Pergamon, Oxford, 1980).
- [21] N. D. Mermin, Phys. Rev. A 176, 250 (1968).
- [22] The Mermin’s proof does not concern the case of the hard body systems. For hard discs the loga rithmic divergence has been demonstrated, in: D. A. Young, B. J. Alder, J. Chem Phys. 60, 1254 (1974).
- [23] J. M. Kosterlitz and D. J. Thouless, J. Phvs. C 6, 1181 (1973); Prog. Low Temp. Phvs. B 7, 371 (1978).
- [24] J. A. Barker and D. Henderson, Rev. Mod. Phvs. 48, 587 (1976).
- [25] F. F. Abraham, Phvs. Rep. 80, 339 (1981).
- [26] K. J. Strandburg, Rev. Mod. Phvs. 60, 161 (1988).
- [27] M. A. Glaser and N. A. Clark, in Advances in Chemical Physics, Volume LXXXIII, Ed. I. Prigogine and S. A. Rice (Wilev, 1993).
- [28] C. Udink and J. van der Elsken, Phvs. Rev. B 35, 279 (1987).
- [29] C. Udink and D. Frenkel, Phys. Rev. B 35, 6933 (1987).
- [30] D. R. Nelson and B. I. Halperin, Phvs. Rev. B 19, 2457 (1979).
- [31] A. P. Young, Phys. Rev. B 19, 1855 (1979).
- [32] R. Pindak et ai, Phys. Rev. Lett. 46, 1135 (1981); S. B. Dierker et al, Phys. Rev. Lett. 56, 1819 (1986); J. D. Brock et al., Phvs. Rev. Lett. 57, 98 (1986); A. Aharonv et al, Phvs. Rev. Lett. 46, 1012 (1986).
- [33] H. Kleinert, Phys. Lett. A 130, 443 (1988).
- [34] W. Janke and H. Kleinert, Phvs. Rev. Lett. 61, 2344 (1988).
- [35] D. R. Nelson and B. I. Halperin, Phys. Rev. B 21, 5312 (1980).
- [36] M. J. P. Gingras, P. C. W. Holdsworth, and B. Bergersen, Phys. Rev. A, 6786 (1990); see also the references therein.
- [37] J. G. Kirkwood, J. Chem. Phys. 18, 380 (1950).
- [38] K. W. Wojciechowski, On the free volume approximation for some anisotropic hard bodies, unpublished.
- [39] A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 61, 2635 (1988); ibid. 63, 1195 (1989).
- [40] J. Lee and J. M. Kosterlitz, Phys. Rev. Lett. 65, 137 (1990).
- [41] J. A. C. Veerman and D. Frenkel, Phys. Rev. A 41, 3237 (1990).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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