×

New universality classes in “percolative” dynamics. (English) Zbl 0945.82529

Summary: We study a site analogue of directed percolation. Random trajectories are generated and their critical behavior is studied. It corresponds to that of simple percolation in some of the parameter spaces, but elsewhere the exponents reveal new universality classes. As a byproduct, we use the model to make an improved estimate of the percolation hull exponents and to calculate the site percolation probability for the square lattice.

MSC:

82B43 Percolation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] D. Stauffer,Introduction to Percolation Theory (Taylor and Francis, London, 1985). · Zbl 0990.82530
[2] G. Grimmett,Percolation (Springer-Verlag, Berlin, 1989).
[3] J. M. F. Gunn and M. Ortuño,J. Phys. A 18:L1095 (1985). · doi:10.1088/0305-4470/18/17/006
[4] B. Y. Bologurov,Sov. Phys. Solid State 28:1694 (1986).
[5] S. N. Dorogostev,Sov. Phys. Solid State 28:1699 (1986).
[6] S. S. Manna and A. J. Guttmann,J. Phys. A 22:3113 (1989). · doi:10.1088/0305-4470/22/15/025
[7] R. M. Bradley,Phys. Rev. A 41:914 (1990). · doi:10.1103/PhysRevA.41.914
[8] I. Majid, N. Jan, A. Coniglio, and H. E. Stanley,Phys. Rev. Lett. 52:1257 (1984); S. Hemmer and P. C. Hemmer,J. Chem. Phys. 81:584 (1984); J. W. Lyklema and K. Kremer,J. Phys. A 17:L691 (1984). · doi:10.1103/PhysRevLett.52.1257
[9] S. Roux, E. Guyon, and D. Sornette,J. Phys. A 21:L475 (1988). · doi:10.1088/0305-4470/21/8/008
[10] B. Duplantier,J. Phys. A 21:3969 (1988). · doi:10.1088/0305-4470/21/20/016
[11] P. Grassberger,J. Phys. A 19:2675 (1986). · Zbl 0605.94003 · doi:10.1088/0305-4470/19/13/032
[12] B. Sapoval, M. Rosso, and J. F. Gouyet,J. Phys. (Paris)46:1149 (1985).
[13] H. Saleur and B. Duplantier,Phys. Rev. Lett. 58:2325 (1987). · doi:10.1103/PhysRevLett.58.2325
[14] R. M. Ziff, P. T. Cummings, and G. Stell,J. Phys. A 17:3009 (1984). · doi:10.1088/0305-4470/17/15/018
[15] A. Weinrib and S. A. Trugman,Phys. Rev. B 31:2993 (1985). · doi:10.1103/PhysRevB.31.2993
[16] R. M. Ziff,Phys. Rev. Lett. 56:545 (1986). · doi:10.1103/PhysRevLett.56.545
[17] J. Salmerón, M. Ortuño, and J. M. F. Gunn,Z. Phys. B 70:269 (1988). · doi:10.1007/BF01318308
[18] T. Gebele,J. Phys. A 17:L51 (1984). · doi:10.1088/0305-4470/17/2/005
[19] M. Rosso, J. F. Gouyet, and B. Sapoval,Phys. Rev. B 32:6053 (1985). · doi:10.1103/PhysRevB.32.6053
[20] M. Ortuño, J. F. M. Gunn, and R. Chicón,J. Phys. A 20:4047 (1987). · doi:10.1088/0305-4470/20/12/050
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.