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Percolation of polyatomic species on a simple cubic lattice

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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.

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References

  1. H. Kesten, Percolation Theory for Mathematicians (Birkhäuser, Boston, 1982)

  2. R. Zallen, The Physics of Amorphous Solids (John Wiley & Sons, New York, 1983)

  3. D. Stauffer, A. Aharony, Introduction to Percolation Theory, 2nd edn. (Taylor & Francis, London, 1985)

  4. M. Sahimi, Applications of Percolation Theory (Taylor & Francis, London, 1994)

  5. M. Sahimi, Flow and transport in Porous Media and Fractured Rock (VCH, Weinheim, 1995)

  6. G. Grimmett, Percolation (Springer-Verlag, Berlin, 1999)

  7. B. Bollobás, O. Riordan, Percolation (Cambridge University Press, New York, 2006)

  8. Y. Gazit, D.A. Berk, M. Leunig, L.T. Baxter, R.K. Jain, Phys. Rev. Lett. 75, 2428 (1995)

    Article  ADS  Google Scholar 

  9. J.W. Baish, Y. Gazit, D.A. Berk, M. Nozue, L.T. Baxter, R.K. Jain, Microvasc. Res. 51, 327 (1996)

    Article  Google Scholar 

  10. D.S. Callaway, M.E.J. Newman, S.H. Strogatz, D.J. Watts, Phys. Rev. Lett. 85, 5468 (2000)

    Article  ADS  Google Scholar 

  11. S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, Rev. Mod. Phys. 80, 1275 (2008)

    Article  ADS  Google Scholar 

  12. A. Bashan, R. Parshani, S. Havlin, Phys. Rev. E 83, 051127 (2011)

    Article  ADS  Google Scholar 

  13. R.K. Pan, M. Kivelä, J. Saramäki, K. Kaski, J. Kertész, Phys. Rev. E 83, 046112 (2011)

    Article  ADS  Google Scholar 

  14. A. Yazdi, H. Hamzehpour, M. Sahimi, Phys. Rev. E 84, 046317 (2011)

    Article  ADS  Google Scholar 

  15. S. Kirkpatrick, Rev Mod. Phys. 45, 574 (1973)

    Article  ADS  Google Scholar 

  16. C. Moore, M.E.J. Newman, Phys. Rev. E 61, 5678 (2000)

    Article  ADS  Google Scholar 

  17. C.L. Henley, Phys. Rev. Lett. 71, 2741 (1993)

    Article  ADS  Google Scholar 

  18. N. Zekri, L. Zekri, C. Lallemand, Y. Pizzo, A. Kaiss, J.-P. Clerc, B. Porterie, J. Phys.: Conf. Ser. 395, 012010 (2012)

    Article  ADS  Google Scholar 

  19. E. Kenah, J.M. Robins, Phys. Rev. E 76, 036113 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  20. R. Cohen, K. Erez, D. ben-Avraham, S. Havlin, Phys. Rev. Lett. 85, 4626 (2000)

    Article  ADS  Google Scholar 

  21. M. Adam, M. Delsanti, D. Durand, G. Hild, J.P. Munch, Pure Appl. Chem. 53, 1489 (1981)

    Article  Google Scholar 

  22. Y. Chen, G. Paul, R. Cohen, S. Havlin, S. P. Borgatti, F. Liljeros, H.E. Stanley, Phys. Rev. E 75, 046107 (2007)

    Article  ADS  Google Scholar 

  23. S. Solomon, G. Weisbuch, L. de Arcangelis, N. Jan, D. Stauffer, Physica A 277, 239 (2000)

    Article  ADS  Google Scholar 

  24. C.M. Fortuin, P.W. Kasteleyn, Physica 57, 536 (1972)

    Article  MathSciNet  ADS  Google Scholar 

  25. A. Coniglio, J. Phys.: Condens. Matter 13, 9039 (2001)

    Article  ADS  Google Scholar 

  26. S.R. Broadbent, J.M. Hammersley, Proc. Cambridge Phil. Soc. 53, 629 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. J.M. Hammersley, Proc. Cambridge Phil. Soc. 53, 642 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. H.L. Frisch, J.M. Hammersley, J. Soc. Ind. Appl. Math. 11, 894 (1963)

    Article  MathSciNet  Google Scholar 

  29. P. Agrawal, S. Redner, P.J. Reynolds, H.E. Stanley, J. Phys. A 12, 2073 (1979)

    Article  ADS  Google Scholar 

  30. V. Cornette, A.J. Ramirez-Pastor, F. Nieto, Physica A 327, 71 (2003)

    Article  ADS  MATH  Google Scholar 

  31. V. Cornette, A.J. Ramirez-Pastor, F. Nieto, Eur. Phys. J. B 36, 391 (2003)

    Article  ADS  Google Scholar 

  32. V. Cornette, A.J. Ramirez-Pastor, F. Nieto, Phys. Lett. A 353, 452 (2006)

    Article  ADS  Google Scholar 

  33. V. Cornette, A.J. Ramirez-Pastor, F. Nieto, J. Chem. Phys. 125, 204702 (2006)

    Article  ADS  Google Scholar 

  34. V.A. Cherkasova, Y.Y. Tarasevich, N.I. Lebovka, N.V. Vygornitskii, Eur. Phys. J. B 74, 205 (2010)

    Article  ADS  Google Scholar 

  35. M. Dolz, F. Nieto, A.J. Ramirez-Pastor, Eur. Phys. J. B 43, 363 (2005)

    Article  ADS  Google Scholar 

  36. M. Dolz, F. Nieto, A.J. Ramirez-Pastor, Phys. Rev. E 72, 066129 (2005)

    Article  ADS  Google Scholar 

  37. M. Dolz, F. Nieto, A.J. Ramirez-Pastor, Physica A 374, 239 (2007)

    Article  ADS  Google Scholar 

  38. P. Longone, P.M. Centres, A.J. Ramirez-Pastor, Phys. Rev. E 85, 011108 (2012)

    Article  ADS  Google Scholar 

  39. Y.Y. Tarasevich, V.A. Cherkasova, Eur. Phys. J. B 60, 97 (2007)

    Article  ADS  Google Scholar 

  40. Y.Y. Tarasevich, N.I. Lebovka, V.V. Laptev, Phys. Rev. E 86, 061116 (2012)

    Article  ADS  Google Scholar 

  41. K. Binder, Rep. Prog. Phys. 60, 488 (1997)

    Article  ADS  Google Scholar 

  42. F. Yonezawa, S. Sakamoto, M. Hori, Phys. Rev. B 40, 636 (1989)

    Article  ADS  Google Scholar 

  43. F. Yonezawa, S. Sakamoto, M. Hori, Phys. Rev. B 40, 650 (1989)

    Article  ADS  Google Scholar 

  44. S. Biswas, A. Kundu, A.K. Chandra, Phys. Rev. E 83, 021109 (2011)

    Article  ADS  Google Scholar 

  45. A.K. Chandra, Phys. Rev. E 85, 021149 (2012)

    Article  ADS  Google Scholar 

  46. J. Hoshen, R. Kopelman, Phys. Rev. B 14, 3438 (1976)

    Article  ADS  Google Scholar 

  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

  48. M.E.J. Newman, R.M. Ziff, Phys. Rev. Lett. 85, 4104 (2000)

    Article  ADS  Google Scholar 

  49. S. Fortunato, Phys. Rev. B 67, 014102 (2003)

    Article  ADS  Google Scholar 

  50. S. Fortunato, Phys. Rev. B 66, 054107 (2002)

    Article  ADS  Google Scholar 

  51. W. Selke, L.N. Shchur, J. Phys. A 38, L739 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. W. Selke, J. Stat. Mech.: Theory Exp. 2007, P04008 (2007)

    Article  Google Scholar 

  53. A. Bunde, S. Havlin, Fractals and Disordered Systems (Springer, Heidelberg, 1996)

  54. Y. Deng, H.W.J. Blöte, Phys. Rev. E 72, 016126 (2005)

    Article  ADS  Google Scholar 

  55. D.A. Matoz-Fernandez, D.H. Linares, A.J. Ramirez-Pastor, Eur. Phys. J. B 85, 296 (2012)

    Article  ADS  Google Scholar 

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Garcia, G., Sanchez-Varretti, F., Centres, P. et al. Percolation of polyatomic species on a simple cubic lattice. Eur. Phys. J. B 86, 403 (2013). https://doi.org/10.1140/epjb/e2013-40509-1

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