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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.M. Hammersley, Proc. Cambridge Phil. Soc. 53, 642 (1957)
D. Stauffer, Introduction to Percolation Theory (Taylor & Francis, 1985)
R. Zallen, The Physics of Amorphous Solids (John Willey & Sons, NY, 1983)
J.W. Essam, Reports on Progress in Physics 43, 833 (1980)
K. Binder, Reports on Progress in Physics 60, 488 (1997)
C. Lorenz, R. May, R. Ziff, J. Stat. Phys. 98, 961 (2000)
M. Aizenman, Nuclear Phys. B 485, 551 (1997)
J. Cardy, J. Phys. A 31, L105 (1998)
L.N. Shchur, S.S. Kosyakov, Int. J. Mod. Phys. C 8, 473 (1997)
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)
A. Coniglio, H.E. Stanley, W. Klein, Phys. Rev. Lett. 42, 518 (1979)
H.L. Frisch, J.M. Hammersley, J. Soc. Ind. Appl. Math. 11, 894 (1963)
P. Agrawal, S. Render, P.J. Reynolds, H.E. Stanley, J. Phys. A: Math. Gen. 12, 2073 (1979)
H. Nakanishi, J. Reynolds, Phys. Lett. 71 A, 252 (1979)
M. Yanuka, R. Englman, J. Phys. A: Math. Gen. 23, L339 (1990)
Y.Y. Tarasevich, S.C. van der Marck, Int. J. Mod. Phys. C 10, 1193 (1999)
W. Kinzel, Directed Percolation, in Percolation Structures and Processes, edited by G. Deutscher, R. Zallen, J. Adler (Hilger, Bristol, 1983)
P. Grassberger, A. de la Torre, Ann. Phys. N.Y. 122, 373 (1979)
P. Grassberger, K. Sundermeyer, Phys. Lett. B 77, 220 (1978)
K. De’Bell, J.W. Essam, J. Phys. A: Math. Gen. 18, 355 (1985)
A. Tretyakov, N. Inui, J. Phys. A: Math. Gen. 28, 3985 (1995)
J.W. Evans, D.E. Sanders, Phys. Rev. B 39, 1587 (1989)
H. Harder, A. Bunde, W. Dieterich, J. Chem. Phys. 85, 4123 (1986)
H. Holloway, Phys. Rev. B 37, 874 (1988)
M. Henkel, F. Seno, Phys. Rev. E 53, 3662 (1996)
E.L. Hinrichsen, J. Feder, T. Jossang, J. Stat. Phys. 44, 793 (1986)
Y. Leroyer, E. Pommiers, Phys. Rev. B 50, 2795 (1994)
B. Bonnier, M. Honterbeyrie, Y. Leroyer, C. Meyers, E. Pommiers, Phys. Rev. B 49, 305 (1994)
Z. Gao, Z.R. Yang, Physica A 255, 242 (1998)
V. Cornette, A.J. Ramirez-Pastor, F. Nieto, Physica A 327, 71 (2003)
V. Cornette, A.J. Ramirez-Pastor, F. Nieto, Eur. Phys. J. B 36, 391 (2003)
R.M. Ziff, E. Gulari, Y. Barshad, Phys. Rev. Lett. 56, 2553 (1986), and references therein
C.T. Rettner, H. Stein, Phys. Rev. Lett. 59, 2768 (1987)
C.T. Rettner, C.B. Mullins, J. Chem. Phys. 94, 1626 (1991)
J.E. Davis, P.D. Nolan, S.G. Karseboom, C.B. Mullins, J. Chem. Phys. 107, 943 (1997)
J. Hoshen, R. Kopelman, Phys. Rev. B 14, 3438 (1976); J. Hoshen, R. Kopelman, E.M. Monberg, J. Stat. Phys. 19, 219 (1978)
F. Yonezawa, S. Sakamoto, M. Hori, Phys. Rev. B 40, 636 (1989)
F. Yonezawa, S. Sakamoto, M. Hori, Phys. Rev. B 40, 650 (1989)
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dolz, M., Nieto, F. & Ramirez-Pastor, A. Dimer site-bond percolation on a square lattice. Eur. Phys. J. B 43, 363–368 (2005). https://doi.org/10.1140/epjb/e2005-00064-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2005-00064-0