Abstract
We investigate the dynamics of a three-state stochastic lattice gas consisting of holes and two oppositely “charged” species of particles, under the influence of an “electric” field at zero total charge. Interacting only through an excluded-volume constraint, particles exchange with holes and, on a slower time scale, with each other. Using a combination of Monte Carlo simulations and meanfield equations of motion, we study a set of suitably defined order parameters, their histograms and fluctuations, as well as the current through the system. With increasing particle density and drive, the system first orders into a charge-segregated state, and then disorders again near complete filling. The transition is first order at low densities and turns second order at higher ones. The finite-size and aspect-ratio dependence of characteristic quantities is discussed at the mean-field level.
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References
B. Schmittmann and R. K. P. Zia, InPhase Transitions and Critical Phenomena, Vol. 17, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1995).
S. Katz, J. L. Lebowitz, and H. Spohn,Phys. Rev. B 28:1655 (1983);J. Stat. Phys. 34:497 (1984).
P. C. Martin, E. D. Siggia, and H. H. Rose,Phys. Rev. A 8: 423 (1973); H. K. Janssen,Z. Phys. B 23: 377 (1976); C. de Dominicis,J. Phys. (Paris)Colloq. 37: C247 (1976); R. Bausch, H. K. Janssen, and H. Wagner,Z. Phys. B 24: 113 (1976).
H. K. Janssen and B. Schmittmann,Z. Phys. B 64: 503 (1986); K.-T. Leung and J. L. Cardy,J. Stat. Phys. 44: 567, 1087 (1986).
K.-t. Leung,Phys. Rev. Lett. 66: 453 (1991);Int. J. Mod. Phys. C 3: 367 (1992).
S. Chandra,Superionic Solids. Principles and Applications (North-Holland, Amsterdam, 1981).
M. Aertsens and J. Naudts,J. Stat. Phys. 62: 609 (1990).
M. Rubinstein,Phys. Rev. Lett. 59: 1946 (1987); T. A. J. Duke,Phys. Rev. Lett. 62: 2877 (1989); Y. Shnidman, InMathematics in Industrial Problems IV, A. Friedman, ed. (Springer, Berlin, 1991); B. Widom, J. L. Viovy, and A. D. Desfontaines,J. Phys. I (France)1: 1759 (1991).
O. Biham, A. A. Middleton, and D. Levine,Phys. Rev. A 46: R6124 (1992); J. A. Cuesta, F. C. Martinez, J. M. Molera, and A. Sánchez,Phys. Rev. E 48: R4176 (1993); K.-t. Leung,Phys. Rev. Lett. 73: 2386 (1994); J. M. Molera, F. C. Martínez, and J. A. Cuesta,Phys. Rev. E 51: 175 (1995).
R. B. Potts,Proc. Camb. Phil. Soc. 48: 106 (1952); F. Y. Wu,Rev. Mod. Phys. 54: 235 (1982).
J. Ashkin and E. Teller,Phys. Rev. 64: 178 (1943).
M. Blume, V. J. Emery, and R. B. Griffiths,Phys. Rev. A 4: 1071 (1971).
W. Selke, InPhase Transitions and Critical Phenomena, Vol. 15 C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1993).
B. Schmittmann, K. Hwang, and R. K. P. Zia,Europhys. Lett. 19: 19 (1992).
D. P. Foster and C. Godrèche,J. Stat. Phys. 76: 1129 (1994).
K. E. Bassler, B. Schmittmann, and R. K. P. Zia,Europhys. Lett. 24: 115 (1993).
V. Becker and H. K. Janssen,Europhys. Lett. 19: 13 (1992).
B. Derrida, S. A. Janowsky, J. L. Lebowitz, and E. R. Speer,Europhys. Lett. 22: 651 (1993);J. Stat. Phys. 73: 813 (1993).
M. R. Evans, D. P. Foster, C. Godrèche, and D. Mukamel,Phys. Rev. Lett. 78: 208 (1995);J. Stat. Phys. 80: 69 (1995).
F. Spitzer,Adv. Math. 5: 246 (1970).
G. Korniss, B. Schmittmann, and R. K. P. Zia,Europhys. Lett. 32: 49 (1995).
I. Vilfan, R. K. P. Zia, and B. Schmittmann,Phys. Rev. Lett. 73: 2071 (1994).
G. Korniss, B. Schmittmann, and R. K. P. Zia, to be published inPhysica A (1997).
R. K. P. Zia and B. Schmittmann, Novel Goldstone modes in biased diffusion of two species, to be published.
H. Haken,Synergetics, An Introduction, 3rd ed. (Springer, Berlin, 1983).
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Korniss, G., Schmittmann, B. & Zia, R.K.P. Nonequilibrium phase transitions in a simple three-state lattice gas. J Stat Phys 86, 721–748 (1997). https://doi.org/10.1007/BF02199117
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DOI: https://doi.org/10.1007/BF02199117