Stationary state in a two-temperature model with competing dynamics

Attila Szolnoki

doi:10.1103/PhysRevE.60.2425

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Stationary state in a two-temperature model with competing dynamics

Attila Szolnoki

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

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Phys. Rev. E 60, 2425 – Published 1 August, 1999

DOI: https://doi.org/10.1103/PhysRevE.60.2425

Abstract

A two-dimensional half-filled lattice gas model with nearest-neighbor attractive interaction is studied where particles are coupled to two thermal baths at different temperatures $T_{1}$ and $T_{2} .$ The hopping of particles is governed by the heat bath at temperature $T_{1}$ with probability p and the other heat bath ${(T}_{2})$ with probability $1 - p$ independently of the hopping direction. On a square lattice the vertical and horizontal interfaces become unstable while interfaces are stable in the diagonal directions. As a consequence, particles condense into a tilted square in the novel ordered state. The p dependence of the resulting nonequilibrium stationary state is studied by a Monte Carlo simulation and dynamical mean-field approximation as well.

References (18)

For a brief review, see Z. Rácz and R. K. P. Zia, Phys. Rev. E 49, 139 (1994).
P. L. Garrido, A. Labarta, and J. Marro, J. Stat. Phys. 49, 551 (1987).
A. De Masi, P. A. Ferrari, and J. L. Lebowitz, Phys. Rev. Lett. 55, 1947 (1987).
S. Katz, J. L. Lebowitz, and H. Spohn, Phys. Rev. B 28, 1655 (1983).
P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990).
R. Dickman, Phys. Rev. A 38, 2588 (1988).
T. Tomé, M. J. de Oliveira, and M. A. Santos, J. Phys. A 24, 3677 (1991).
A. Szolnoki, G. Szabó, and O. G. Mouritsen, Phys. Rev. E 55, 2255 (1997).
B. C. S. Grandi and W. Figueiredo, Phys. Rev. E 56, 5240 (1997).
S. C. Glotzer, D. Stauffer, and N. Jan, Phys. Rev. Lett. 72, 4109 (1994).
T. Tomé and M. J. de Oliveira, Phys. Rev. A 40, 6643 (1989).
H.-J. Xu, B. Bergersen, and Z. Rácz, Phys. Rev. E 47, 1520 (1993).
J. Marro, A. Achahbar, P. L. Garrido, and J. J. Alonso, Phys. Rev. E 53, 6038 (1996).
A. Szolnoki, J. Phys. A 30, 7791 (1997).
G. Grinstein, C. Jayaprakash, and Y. He, Phys. Rev. Lett. 55, 2527 (1985).
F. J. Alexander, C. A. Laberge, J. L. Lebowitz, and R. K. P. Zia, J. Stat. Phys. 82, 1133 (1996); S. Toxvaerd, Phys. Rev. E 53, 3710 (1996).
M. C. Sabra, H. Gilhøj, and O. G. Mouritsen, Phys. Rev. E 58, 3547 (1998), and references therein.
G. Szabó, A. Szolnoki, and T. Antal, Phys. Rev. E 49, 299 (1994); ibid.G. Szabó, A. Szolnoki, T. Antal, and I. Borsos, 55, 5275 (1997).

[c1] For a brief review, see Z. Rácz and R. K. P. Zia, Phys. Rev. E 49, 139 (1994).

[c2] P. L. Garrido, A. Labarta, and J. Marro, J. Stat. Phys. 49, 551 (1987).

[c3] A. De Masi, P. A. Ferrari, and J. L. Lebowitz, Phys. Rev. Lett. 55, 1947 (1987).

[c4] S. Katz, J. L. Lebowitz, and H. Spohn, Phys. Rev. B 28, 1655 (1983).

[c5] P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42, 1954 (1990).

[c6] R. Dickman, Phys. Rev. A 38, 2588 (1988).

[c7] T. Tomé, M. J. de Oliveira, and M. A. Santos, J. Phys. A 24, 3677 (1991).

[c8] A. Szolnoki, G. Szabó, and O. G. Mouritsen, Phys. Rev. E 55, 2255 (1997).

[c9] B. C. S. Grandi and W. Figueiredo, Phys. Rev. E 56, 5240 (1997).

[c10] S. C. Glotzer, D. Stauffer, and N. Jan, Phys. Rev. Lett. 72, 4109 (1994).

[c11] T. Tomé and M. J. de Oliveira, Phys. Rev. A 40, 6643 (1989).

[c12] H.-J. Xu, B. Bergersen, and Z. Rácz, Phys. Rev. E 47, 1520 (1993).

[c13] J. Marro, A. Achahbar, P. L. Garrido, and J. J. Alonso, Phys. Rev. E 53, 6038 (1996).

[c14] A. Szolnoki, J. Phys. A 30, 7791 (1997).

[c15] G. Grinstein, C. Jayaprakash, and Y. He, Phys. Rev. Lett. 55, 2527 (1985).

[c16] F. J. Alexander, C. A. Laberge, J. L. Lebowitz, and R. K. P. Zia, J. Stat. Phys. 82, 1133 (1996); S. Toxvaerd, Phys. Rev. E 53, 3710 (1996).

[c17] M. C. Sabra, H. Gilhøj, and O. G. Mouritsen, Phys. Rev. E 58, 3547 (1998), and references therein.

[c18] G. Szabó, A. Szolnoki, and T. Antal, Phys. Rev. E 49, 299 (1994); ibid.G. Szabó, A. Szolnoki, T. Antal, and I. Borsos, 55, 5275 (1997).

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