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Asymptotic behavior of the entropy of chains placed on cylinders

W. G. Dantas* and M. J. de Oliveira†

J. F. Stilck‡

  • Universidade de São Paulo, Caixa Postal 66318 05315-970 São Paulo, São Paulo, Brazil

  • Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/n, 24210-340, Niterói, RJ, Brazil

  • *wgd@gibbs.if.usp.br
  • †oliveira@if.usp.br
  • ‡jstilck@if.uff.br
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Phys. Rev. E 76, 031133 – Published 27 September, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.031133

Abstract

By using the transfer matrix approach, we investigate the asymptotic behavior of the entropy of flexible chains with M monomers each placed on strips with periodic boundary conditions (cylinders). In the limit of high density of monomers, we study the behavior of the entropy as a function of the density of monomers and the width of the strip, inspired by recent analytical studies of this problem for the particular case of dimers (M=2). We obtain the entropy in the asymptotic regime of high densities for chains with M=2,…,9 monomers, as well as for the special case of polymers, where M→∞, and find that the results show a regular behavior similar to the one found analytically for dimers. We also verify that in the low-density limit the mean-field expression for the entropy is followed by the results from our transfer matrix calculations.

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References (20)

  1. R. H. Fowler and G. S. Rushbrooke, Trans. Faraday Soc. 33, 1272 (1937).
  2. P. W. Kasteleyn, J. Math. Phys. 4, 287 (1963).
  3. M. E. Fisher, J. Math. Phys. 7, 1776 (1966).
  4. C. Fan and F. Wu, Phys. Rev. B 2, 723 (1970).
  5. S. R. Salinas and J. F. Nagle, Phys. Rev. B 9, 4920 (1974).
  6. J. F. Nagle, C. S. O. Yokoi, and S. M. Battacharjee, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic Press, New York, 1989), Vol. 13.
  7. M. E. Fisher, Phys. Rev. 124, 1664 (1961).
  8. P. W. Kasteleyn, Physica (Amsterdam) 27, 1209 (1961).
  9. H. N. V. Temperley and M. E. Fisher, Philos. Mag. 6, 1061 (1961).
  10. W. J. Tzeng and F. Y. Wu, J. Stat. Phys. 110, 671 (2003).
  11. F. Y. Wu, Phys. Rev. E 74, 020104(R) (2006); 74, 039907(E) (2006).
  12. W. G. Dantas and J. F. Stilck, Phys. Rev. E 67, 031803 (2003).
  13. R. Pemantle and M. C. Wilson, J. Comb. Theory, Ser. A 97, 129 (2002).
  14. Y. Kong, Phys. Rev. E 75, 051123 (2007).
  15. Y. Kong, Phys. Rev. E 74, 011102 (2006).
  16. Y. Kong, Phys. Rev. E 74, 061102 (2006).
  17. B. Derrida, J. Phys. A 14, L5 (1981).
  18. P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953).
  19. J. F. Stilck and M. J. de Oliveira, Phys. Rev. A 42, 5955 (1990).
  20. A. Ghosh and D. Dhar, Europhys. Lett. 78, 20003 (2007).

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Phys. Rev. E 76, 031133– Published 27 September, 2007
  • Received 27 June 2007

© 2007 American Physical Society

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