Abstract
We report on a Monte Carlo study of ordering in a nonequilibrium system. The system is a lattice gas that comprises two equal, parallel square lattices with stochastic particle-conserving irreversible dynamics. The particles are driven along a principal direction under the competition of the heat bath and a large, constant external electric field. There is attraction only between particles on nearest-neighbor sites within the same lattice. Particles may jump from one plane to the other; therefore, density fluctuations have an extra mechanism to decay and build up. It helps to obtain the steady-state accurately. Spatial correlations decay with distance according to a power law at high enough temperature, as for the ordinary two-dimensional case. We find two kinds of nonequilibrium phase transitions. The first one has a critical point for half occupation of the lattice, and seems to be related to the anisotropic phase transition reported before for the plane. This transition becomes discontinuous for low enough density. The difference of density between the planes changes discontinuously for any density at a lower temperature. This seems to correspond to a phase transition that does not have a counterpart in equilibrium nor in the two-dimensional nonequilibrium case.
Similar content being viewed by others
References
P. L. Garrido, J. Marro, and R. Dickman,Ann. Phys. (NY)199:366 (1990), and references therein.
H. Spohn,Large Scale Dynamics of Interacting Particles (Springer-Verlag, Berlin, 1991), and references therein.
J. Marro, P. L. Garrido, and J. L. Vallés,Phase Transitions 29:129 (1991), and references therein.
S. Katz, J. L. Lebowitz, and H. Spohn,J. Stat. Phys. 34:497 (1984).
J. Marro, J. L. Lebowitz, H. Spohn, and M. H. Kalos,J. Stat. Phys. 38:725 (1985).
J. L. Vallés and J. Marro,J. Stat. Phys. 43:441 (1986).
J. L. Vallés and J. Marro,J. Stat. Phys. 49:89 (1987).
J. Marro and J. L. Vallés,J. Stat. Phys. 49:121 (1987).
J. S. Wang, K. Binder, and J. L. Lebowitz,J. Stat. Phys. 56:783 (1989).
K. Leung,Phys. Rev. Lett. 66:453 (1991); see also K. Leung,Int. J. Mod. Phys. C 3: 367 (1992), and references therein.
K. Gawadzki and A. Kupiainen,Nucl. Phys. B 269:45 (1986).
H. K. Janssen and B. Schmittmann,Z. Phys. B 64:503 (1986).
K. Leung and J. L. Cardy,J. Stat. Phys. 44:567 (1986).
A. Achahbar, P. L. Garrido, and J. Marro, to be published.
C. N. Yang and T. D. Lee,Phys. Rev. 87:404, 410 (1952).
Z. Cheng, P. L. Garrido, J. L. Lebowitz, and J. L. Vallés,Europhys. Lett. 14: 507 (1991).
J. L. Vallés,J. Phys. I (Paris)2:1361 (1992).
F. J. Alexander, I. Edrei, P. L. Garrido, and J. L. Lebowitz,J. Stat. Phys. 68: 497 (1992).
E. L. Praestgaard, H. Larsen, and R. K. P. Zia,Europhys. Lett. 25:447 (1994).
B. Schmittmann and R. K. P. Zia,Phys. Rev. Lett. 66:357 (1991).
C. K. Chan and L. Lin,Europhys. Lett. 11:13 (1990).
J. Marro, P. L. Garrido, A. Labarta, and R. Toral,J. Phys.: Condensed Matter 1:8147 (1989).
P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn,Phys. Rev. A 42:1954 (1990).
K. Binder and J. S. Wang,J. Stat. Phys. 55:87 (1989).
S. M. Bhattacharjee and J. F. Nagle,Phys. Rev. A 31:3199 (1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Achahbar, A., Marro, J. Phase transitions in a driven lattice gas in two planes. J Stat Phys 78, 1493–1520 (1995). https://doi.org/10.1007/BF02180140
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02180140