Advertisement

Dimer site-bond percolation on a square lattice

  • M. Dolz
  • F. Nieto
  • A. J. Ramirez-PastorEmail author
Statistical and Nonlinear Physics

Abstract.

A generalization of the pure site and pure bond percolation problems in which pairs of nearest neighbor sites (site dimers) and linear pairs of nearest neighbor bonds (bond dimers) are independently occupied at random on a square lattice is studied. We called this model as dimer site-bond percolation. Motivated by considerations of cluster connectivity, we have used two distinct schemes (denoted as \(S\cap B\) and \(S\cup B\)) for dimer site-bond percolation. In \(S \cap B\) (\(S \cup B\)), two points are said to be connected if a sequence of occupied sites and (or) bonds joins them. By using finite-size scaling theory, data from \(S \cap B\) and \(S \cup B\) are analyzed in order to determine i) the phase boundary between the percolating and non-percolating regions and ii) the numerical values of the critical exponents of the phase transition occurring in the system. The results obtained are discussed in comparison with the corresponding ones for classical monomer site-bond percolation.

Keywords

Percolate Critical Exponent Neighbor Site Occupied Site Bond Percolation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.M. Hammersley, Proc. Cambridge Phil. Soc. 53, 642 (1957) CrossRefzbMATHMathSciNetGoogle Scholar
  2. D. Stauffer, Introduction to Percolation Theory (Taylor & Francis, 1985) Google Scholar
  3. R. Zallen, The Physics of Amorphous Solids (John Willey & Sons, NY, 1983) Google Scholar
  4. J.W. Essam, Reports on Progress in Physics 43, 833 (1980) ADSMathSciNetGoogle Scholar
  5. K. Binder, Reports on Progress in Physics 60, 488 (1997)ADSGoogle Scholar
  6. C. Lorenz, R. May, R. Ziff, J. Stat. Phys. 98, 961 (2000) zbMATHGoogle Scholar
  7. M. Aizenman, Nuclear Phys. B 485, 551 (1997) zbMATHADSMathSciNetGoogle Scholar
  8. J. Cardy, J. Phys. A 31, L105 (1998) Google Scholar
  9. L.N. Shchur, S.S. Kosyakov, Int. J. Mod. Phys. C 8, 473 (1997) ADSGoogle Scholar
  10. L.N. Shchur, Incipient Spanning Clusters in Square and Cubic Percolation, in Springer Proceedings in Physics, Vol. 85, edited by D.P. Landau, S.P. Lewis, H.B. Schuettler (Springer Verlag, Heidelberg, Berlin, 2000) Google Scholar
  11. A. Coniglio, H.E. Stanley, W. Klein, Phys. Rev. Lett. 42, 518 (1979) ADSGoogle Scholar
  12. H.L. Frisch, J.M. Hammersley, J. Soc. Ind. Appl. Math. 11, 894 (1963) MathSciNetGoogle Scholar
  13. P. Agrawal, S. Render, P.J. Reynolds, H.E. Stanley, J. Phys. A: Math. Gen. 12, 2073 (1979) ADSGoogle Scholar
  14. H. Nakanishi, J. Reynolds, Phys. Lett. 71 A, 252 (1979) Google Scholar
  15. M. Yanuka, R. Englman, J. Phys. A: Math. Gen. 23, L339 (1990) Google Scholar
  16. Y.Y. Tarasevich, S.C. van der Marck, Int. J. Mod. Phys. C 10, 1193 (1999) ADSGoogle Scholar
  17. W. Kinzel, Directed Percolation, in Percolation Structures and Processes, edited by G. Deutscher, R. Zallen, J. Adler (Hilger, Bristol, 1983) Google Scholar
  18. P. Grassberger, A. de la Torre, Ann. Phys. N.Y. 122, 373 (1979) ADSGoogle Scholar
  19. P. Grassberger, K. Sundermeyer, Phys. Lett. B 77, 220 (1978) ADSGoogle Scholar
  20. K. De’Bell, J.W. Essam, J. Phys. A: Math. Gen. 18, 355 (1985) ADSGoogle Scholar
  21. A. Tretyakov, N. Inui, J. Phys. A: Math. Gen. 28, 3985 (1995) zbMATHADSGoogle Scholar
  22. J.W. Evans, D.E. Sanders, Phys. Rev. B 39, 1587 (1989) ADSGoogle Scholar
  23. H. Harder, A. Bunde, W. Dieterich, J. Chem. Phys. 85, 4123 (1986) ADSGoogle Scholar
  24. H. Holloway, Phys. Rev. B 37, 874 (1988) ADSGoogle Scholar
  25. M. Henkel, F. Seno, Phys. Rev. E 53, 3662 (1996) ADSGoogle Scholar
  26. E.L. Hinrichsen, J. Feder, T. Jossang, J. Stat. Phys. 44, 793 (1986) ADSGoogle Scholar
  27. Y. Leroyer, E. Pommiers, Phys. Rev. B 50, 2795 (1994) ADSGoogle Scholar
  28. B. Bonnier, M. Honterbeyrie, Y. Leroyer, C. Meyers, E. Pommiers, Phys. Rev. B 49, 305 (1994) ADSGoogle Scholar
  29. Z. Gao, Z.R. Yang, Physica A 255, 242 (1998) Google Scholar
  30. V. Cornette, A.J. Ramirez-Pastor, F. Nieto, Physica A 327, 71 (2003) zbMATHADSGoogle Scholar
  31. V. Cornette, A.J. Ramirez-Pastor, F. Nieto, Eur. Phys. J. B 36, 391 (2003) ADSGoogle Scholar
  32. R.M. Ziff, E. Gulari, Y. Barshad, Phys. Rev. Lett. 56, 2553 (1986), and references therein CrossRefADSGoogle Scholar
  33. C.T. Rettner, H. Stein, Phys. Rev. Lett. 59, 2768 (1987) ADSGoogle Scholar
  34. C.T. Rettner, C.B. Mullins, J. Chem. Phys. 94, 1626 (1991) ADSGoogle Scholar
  35. J.E. Davis, P.D. Nolan, S.G. Karseboom, C.B. Mullins, J. Chem. Phys. 107, 943 (1997) ADSGoogle Scholar
  36. J. Hoshen, R. Kopelman, Phys. Rev. B 14, 3438 (1976); J. Hoshen, R. Kopelman, E.M. Monberg, J. Stat. Phys. 19, 219 (1978) ADSGoogle Scholar
  37. F. Yonezawa, S. Sakamoto, M. Hori, Phys. Rev. B 40, 636 (1989) ADSGoogle Scholar
  38. F. Yonezawa, S. Sakamoto, M. Hori, Phys. Rev. B 40, 650 (1989) ADSGoogle Scholar
  39. 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, Vol. 14, Chap. 1 (Academic, NY, 1991), pp. 1134 and 364367 Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidad Nacional de San LuisSan LuisArgentina

Personalised recommendations