Universal behavior of one-dimensional multispecies branching and annihilating random walks with exclusion

Géza Ódor

doi:10.1103/PhysRevE.63.056108

Access by Xinjiang University

Universal behavior of one-dimensional multispecies branching and annihilating random walks with exclusion

Géza Ódor

Research Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary

PDF

Phys. Rev. E 63, 056108 – Published 16 April, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.056108

Abstract

A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching $(\vec{A} A B,$ $\vec{B} B A),$ a continuous phase transition will appear at the zero-branching-rate limit belonging to the same universality class as that of the two component branching and annihilating random-walk model with two symmetric offsprings. This class persists even if the branching is biased towards one of the species. If the two systems are not coupled by branching but a hard-core interaction is allowed only the transition will occur at finite branching rate belonging to the usual $(1 + 1)$ -dimensional directed percolation class.

References (26)

J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999).
H. Hinrichsen, Adv. Phys. 49, 815 (2000).
M. J. Howard and U. C. Täuber, J. Phys. A 30, 7721 (1997).
G. Ódor, Phys. Rev. E 62, R3027 (2000).
H. Hinrichsen, e-print cond-mat/0004348.
S. Kwon, J. Lee, and H. Park, Phys. Rev. Lett. 85, 1682 (2000).
G. Ódor, Phys. Rev. E 63, 021113 (20001).
A. Lipowski, e-print cond-mat/0007411.
U. C. Täuber, M. J. Howard, and H. Hinrichsen, Phys. Rev. Lett. 80, 2165 (1998); ibid.Y. Y. Goldschmidt, 81, 2178 (1998); Y. Y. Goldschmidt, H. Hinrichsen, M. J. Howard, and U. C. Täuber, Phys. Rev. E 59, 6381 (1999); H. K. Janssen, e-print cond-mat/9901188.
H. Hinrichsen and G. Ódor, Phys. Rev. Lett. 82, 1205 (1999).
H. Hinrichsen and G. Ódor, Phys. Rev. E 60, 3842 (1999).
J. E. de Freitas, L. S. Lucena, L. S. da Silva, and H. Hilhorst, Phys. Rev. E 61, 6330 (2000).
F. van Wijland, K. Oerding, and H. Hilhorst, Physica A 251, 179 (1998).
S. Trimpet, U. C. Täuber, and G. M. Schütz, e-print cond-mat/0001387.
H. K. Janssen, Z. Phys. B: Condens. Matter 42, 151 (1981).
P. Grassberger, Z. Phys. B: Condens. Matter 47, 365 (1982).
W. Kinzel, in Percolation Structures and Processes, edited by G. Deutscher, R. Zallen, and J. Adler, [Ann. Isr. Phys. Soc. 5, (1983)].
P. Grassberger, F. Krause, and T. von der Twer, J. Phys. A 17, L105 (1984).
For further references see N. Menyhárd N. and G. Ódor, e-print cond-mat/0001101; Braz. J. Phys. 30, 113 (2000).
J. L. Cardy and U. C. Täuber, J. Stat. Phys. 90, 1 (1998).
H. K. Janssen, e-print cond-mat/0006129.
G. Ódor and N. Menyhárd, Phys. Rev. E 61, 6404 (2000).
G. Mennon, M. Barma, and D. Dhar, J. Stat. Phys. 86, 1237 (1997).
I. Jensen and R. Dickman, Phys. Rev. E 48, 1710 (1993).
M. A. Muñoz, G. Grinstein, R. Dickman, and R. Livi, Phys. Rev. Lett. 76, 451 (1996); Physica D 103, 485 (1997).
I. Jensen, J. Phys. A 32, 5233 (1999).

[c1] J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999).

[c2] H. Hinrichsen, Adv. Phys. 49, 815 (2000).

[c3] M. J. Howard and U. C. Täuber, J. Phys. A 30, 7721 (1997).

[c4] G. Ódor, Phys. Rev. E 62, R3027 (2000).

[c5] H. Hinrichsen, e-print cond-mat/0004348.

[c6] S. Kwon, J. Lee, and H. Park, Phys. Rev. Lett. 85, 1682 (2000).

[c7] G. Ódor, Phys. Rev. E 63, 021113 (20001).

[c8] A. Lipowski, e-print cond-mat/0007411.

[c9] U. C. Täuber, M. J. Howard, and H. Hinrichsen, Phys. Rev. Lett. 80, 2165 (1998); ibid.Y. Y. Goldschmidt, 81, 2178 (1998); Y. Y. Goldschmidt, H. Hinrichsen, M. J. Howard, and U. C. Täuber, Phys. Rev. E 59, 6381 (1999); H. K. Janssen, e-print cond-mat/9901188.

[c10] H. Hinrichsen and G. Ódor, Phys. Rev. Lett. 82, 1205 (1999).

[c11] H. Hinrichsen and G. Ódor, Phys. Rev. E 60, 3842 (1999).

[c12] J. E. de Freitas, L. S. Lucena, L. S. da Silva, and H. Hilhorst, Phys. Rev. E 61, 6330 (2000).

[c13] F. van Wijland, K. Oerding, and H. Hilhorst, Physica A 251, 179 (1998).

[c14] S. Trimpet, U. C. Täuber, and G. M. Schütz, e-print cond-mat/0001387.

[c15] H. K. Janssen, Z. Phys. B: Condens. Matter 42, 151 (1981).

[c16] P. Grassberger, Z. Phys. B: Condens. Matter 47, 365 (1982).

[c17] W. Kinzel, in Percolation Structures and Processes, edited by G. Deutscher, R. Zallen, and J. Adler, [Ann. Isr. Phys. Soc. 5, (1983)].

[c18] P. Grassberger, F. Krause, and T. von der Twer, J. Phys. A 17, L105 (1984).

[c19] For further references see N. Menyhárd N. and G. Ódor, e-print cond-mat/0001101; Braz. J. Phys. 30, 113 (2000).

[c20] J. L. Cardy and U. C. Täuber, J. Stat. Phys. 90, 1 (1998).

[c21] H. K. Janssen, e-print cond-mat/0006129.

[c22] G. Ódor and N. Menyhárd, Phys. Rev. E 61, 6404 (2000).

[c23] G. Mennon, M. Barma, and D. Dhar, J. Stat. Phys. 86, 1237 (1997).

[c24] I. Jensen and R. Dickman, Phys. Rev. E 48, 1710 (1993).

[c25] M. A. Muñoz, G. Grinstein, R. Dickman, and R. Livi, Phys. Rev. Lett. 76, 451 (1996); Physica D 103, 485 (1997).

[c26] I. Jensen, J. Phys. A 32, 5233 (1999).

Physical Review E

Export citation

Export citation

Universal behavior of one-dimensional multispecies branching and annihilating random walks with exclusion

Abstract

References (26)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation