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Percolation of polyatomic species on a simple cubic lattice

  • G.D. Garcia
  • F.O. Sanchez-Varretti
  • P.M. Centres
  • A.J. Ramirez-Pastor
Regular Article

Abstract

In the present paper, the site-percolation problem corresponding to linear k-mers (containing k identical units, each one occupying a lattice site) on a simple cubic lattice has been studied. The k-mers were irreversibly and isotropically deposited into the lattice. Then, the percolation threshold and critical exponents were obtained by numerical simulations and finite-size scaling theory. The results, obtained for k ranging from 1 to 100, revealed that (i) the percolation threshold exhibits a decreasing function when it is plotted as a function of the k-mer size; and (ii) the phase transition occurring in the system belongs to the standard 3D percolation universality class regardless of the value of k considered.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    H. Kesten, Percolation Theory for Mathematicians (Birkhäuser, Boston, 1982) Google Scholar
  2. 2.
    R. Zallen, The Physics of Amorphous Solids (John Wiley & Sons, New York, 1983) Google Scholar
  3. 3.
    D. Stauffer, A. Aharony, Introduction to Percolation Theory, 2nd edn. (Taylor & Francis, London, 1985) Google Scholar
  4. 4.
    M. Sahimi, Applications of Percolation Theory (Taylor & Francis, London, 1994) Google Scholar
  5. 5.
    M. Sahimi, Flow and transport in Porous Media and Fractured Rock (VCH, Weinheim, 1995) Google Scholar
  6. 6.
    G. Grimmett, Percolation (Springer-Verlag, Berlin, 1999) Google Scholar
  7. 7.
    B. Bollobás, O. Riordan, Percolation (Cambridge University Press, New York, 2006) Google Scholar
  8. 8.
    Y. Gazit, D.A. Berk, M. Leunig, L.T. Baxter, R.K. Jain, Phys. Rev. Lett. 75, 2428 (1995) ADSCrossRefGoogle Scholar
  9. 9.
    J.W. Baish, Y. Gazit, D.A. Berk, M. Nozue, L.T. Baxter, R.K. Jain, Microvasc. Res. 51, 327 (1996) CrossRefGoogle Scholar
  10. 10.
    D.S. Callaway, M.E.J. Newman, S.H. Strogatz, D.J. Watts, Phys. Rev. Lett. 85, 5468 (2000) ADSCrossRefGoogle Scholar
  11. 11.
    S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, Rev. Mod. Phys. 80, 1275 (2008) ADSCrossRefGoogle Scholar
  12. 12.
    A. Bashan, R. Parshani, S. Havlin, Phys. Rev. E 83, 051127 (2011) ADSCrossRefGoogle Scholar
  13. 13.
    R.K. Pan, M. Kivelä, J. Saramäki, K. Kaski, J. Kertész, Phys. Rev. E 83, 046112 (2011) ADSCrossRefGoogle Scholar
  14. 14.
    A. Yazdi, H. Hamzehpour, M. Sahimi, Phys. Rev. E 84, 046317 (2011) ADSCrossRefGoogle Scholar
  15. 15.
    S. Kirkpatrick, Rev Mod. Phys. 45, 574 (1973) ADSCrossRefGoogle Scholar
  16. 16.
    C. Moore, M.E.J. Newman, Phys. Rev. E 61, 5678 (2000) ADSCrossRefGoogle Scholar
  17. 17.
    C.L. Henley, Phys. Rev. Lett. 71, 2741 (1993) ADSCrossRefGoogle Scholar
  18. 18.
    N. Zekri, L. Zekri, C. Lallemand, Y. Pizzo, A. Kaiss, J.-P. Clerc, B. Porterie, J. Phys.: Conf. Ser. 395, 012010 (2012) ADSCrossRefGoogle Scholar
  19. 19.
    E. Kenah, J.M. Robins, Phys. Rev. E 76, 036113 (2007) MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    R. Cohen, K. Erez, D. ben-Avraham, S. Havlin, Phys. Rev. Lett. 85, 4626 (2000) ADSCrossRefGoogle Scholar
  21. 21.
    M. Adam, M. Delsanti, D. Durand, G. Hild, J.P. Munch, Pure Appl. Chem. 53, 1489 (1981) CrossRefGoogle Scholar
  22. 22.
    Y. Chen, G. Paul, R. Cohen, S. Havlin, S. P. Borgatti, F. Liljeros, H.E. Stanley, Phys. Rev. E 75, 046107 (2007) ADSCrossRefGoogle Scholar
  23. 23.
    S. Solomon, G. Weisbuch, L. de Arcangelis, N. Jan, D. Stauffer, Physica A 277, 239 (2000) ADSCrossRefGoogle Scholar
  24. 24.
    C.M. Fortuin, P.W. Kasteleyn, Physica 57, 536 (1972) MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    A. Coniglio, J. Phys.: Condens. Matter 13, 9039 (2001) ADSCrossRefGoogle Scholar
  26. 26.
    S.R. Broadbent, J.M. Hammersley, Proc. Cambridge Phil. Soc. 53, 629 (1957) MathSciNetADSCrossRefMATHGoogle Scholar
  27. 27.
    J.M. Hammersley, Proc. Cambridge Phil. Soc. 53, 642 (1957) MathSciNetADSCrossRefMATHGoogle Scholar
  28. 28.
    H.L. Frisch, J.M. Hammersley, J. Soc. Ind. Appl. Math. 11, 894 (1963) MathSciNetCrossRefGoogle Scholar
  29. 29.
    P. Agrawal, S. Redner, P.J. Reynolds, H.E. Stanley, J. Phys. A 12, 2073 (1979) ADSCrossRefGoogle Scholar
  30. 30.
    V. Cornette, A.J. Ramirez-Pastor, F. Nieto, Physica A 327, 71 (2003) ADSCrossRefMATHGoogle Scholar
  31. 31.
    V. Cornette, A.J. Ramirez-Pastor, F. Nieto, Eur. Phys. J. B 36, 391 (2003) ADSCrossRefGoogle Scholar
  32. 32.
    V. Cornette, A.J. Ramirez-Pastor, F. Nieto, Phys. Lett. A 353, 452 (2006) ADSCrossRefGoogle Scholar
  33. 33.
    V. Cornette, A.J. Ramirez-Pastor, F. Nieto, J. Chem. Phys. 125, 204702 (2006) ADSCrossRefGoogle Scholar
  34. 34.
    V.A. Cherkasova, Y.Y. Tarasevich, N.I. Lebovka, N.V. Vygornitskii, Eur. Phys. J. B 74, 205 (2010) ADSCrossRefGoogle Scholar
  35. 35.
    M. Dolz, F. Nieto, A.J. Ramirez-Pastor, Eur. Phys. J. B 43, 363 (2005) ADSCrossRefGoogle Scholar
  36. 36.
    M. Dolz, F. Nieto, A.J. Ramirez-Pastor, Phys. Rev. E 72, 066129 (2005) ADSCrossRefGoogle Scholar
  37. 37.
    M. Dolz, F. Nieto, A.J. Ramirez-Pastor, Physica A 374, 239 (2007) ADSCrossRefGoogle Scholar
  38. 38.
    P. Longone, P.M. Centres, A.J. Ramirez-Pastor, Phys. Rev. E 85, 011108 (2012) ADSCrossRefGoogle Scholar
  39. 39.
    Y.Y. Tarasevich, V.A. Cherkasova, Eur. Phys. J. B 60, 97 (2007) ADSCrossRefGoogle Scholar
  40. 40.
    Y.Y. Tarasevich, N.I. Lebovka, V.V. Laptev, Phys. Rev. E 86, 061116 (2012) ADSCrossRefGoogle Scholar
  41. 41.
    K. Binder, Rep. Prog. Phys. 60, 488 (1997) ADSCrossRefGoogle Scholar
  42. 42.
    F. Yonezawa, S. Sakamoto, M. Hori, Phys. Rev. B 40, 636 (1989) ADSCrossRefGoogle Scholar
  43. 43.
    F. Yonezawa, S. Sakamoto, M. Hori, Phys. Rev. B 40, 650 (1989) ADSCrossRefGoogle Scholar
  44. 44.
    S. Biswas, A. Kundu, A.K. Chandra, Phys. Rev. E 83, 021109 (2011) ADSCrossRefGoogle Scholar
  45. 45.
    A.K. Chandra, Phys. Rev. E 85, 021149 (2012) ADSCrossRefGoogle Scholar
  46. 46.
    J. Hoshen, R. Kopelman, Phys. Rev. B 14, 3438 (1976) ADSCrossRefGoogle Scholar
  47. 47.
    V. Privman, P.C. Hohenberg, A. Aharony, Universal Critical-Point Amplitude Relations, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic, NY, 1991) Vol. 14, Chap. 1 Google Scholar
  48. 48.
    M.E.J. Newman, R.M. Ziff, Phys. Rev. Lett. 85, 4104 (2000) ADSCrossRefGoogle Scholar
  49. 49.
    S. Fortunato, Phys. Rev. B 67, 014102 (2003) ADSCrossRefGoogle Scholar
  50. 50.
    S. Fortunato, Phys. Rev. B 66, 054107 (2002) ADSCrossRefGoogle Scholar
  51. 51.
    W. Selke, L.N. Shchur, J. Phys. A 38, L739 (2005) MathSciNetADSCrossRefMATHGoogle Scholar
  52. 52.
    W. Selke, J. Stat. Mech.: Theory Exp. 2007, P04008 (2007) CrossRefGoogle Scholar
  53. 53.
    A. Bunde, S. Havlin, Fractals and Disordered Systems (Springer, Heidelberg, 1996) Google Scholar
  54. 54.
    Y. Deng, H.W.J. Blöte, Phys. Rev. E 72, 016126 (2005) ADSCrossRefGoogle Scholar
  55. 55.
    D.A. Matoz-Fernandez, D.H. Linares, A.J. Ramirez-Pastor, Eur. Phys. J. B 85, 296 (2012) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • G.D. Garcia
    • 1
  • F.O. Sanchez-Varretti
    • 1
  • P.M. Centres
    • 2
  • A.J. Ramirez-Pastor
    • 2
  1. 1.Universidad Tecnológica Nacional, Facultad Regional San RafaelMendozaArgentina
  2. 2.Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICETSan LuisArgentina

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