Abstract
Based on a high-temperature expansion, we compute the two-point correlation function and the critical line of an Ising lattice gas driven into a nonequilibrium steady state by a uniform bias E. The lowest nontrivial order already reproduces the key features, i.e., the discontinuity singularity of the structure factor and the (qualitative) E dependence of the critical line. Our approach is easily generalized to other nonequilibrium lattice models and provides a simple analytic tool for the study of the high-temperature phase and its boundaries.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
S. Katz, J. L. Lebowitz, and H. Spohn, Phys. Rev. B 28:1655 (1983) and J. Stat. Phys. 34:497 (1984).
B. Schmittmann and R. K. P. Zia, in Phase Transitions and Critical Phenomena, Vol. 17, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1995).
S. Chandra, Superionic Solids. Principles and Applications (North Holland, Amsterdam, 1981).
G. Gompper and M. Schick, in Phase Transitions and Critical Phenomena, Vol. 16, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1994); L. Auvray, in Micelles, Membranes and Monolayers, W. M. Gelbart, A. Ben-Shaul, and D. Roux, eds. (Springer, Berlin, 1994).
C. Domb, in Phase Transitions and Critical Phenomena, Vol. 3, C. Domb and M. Green, eds. (Academic Press, London, 1974).
M. Q. Zhang, J.-S. Wang, J. L. Lebowitz, and J. L. Valles, J. Stat. Phys. 52:1461 (1988). See also P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Phys. Rev. A 42:1954 (1990).
R. K. P. Zia, K. Hwang, B. Schmittmann, and K.-t. Leung, Physica A 194:183 (1993).
R. Kubo, Rep. Progr. Phys. 29:25 1966).
F. Spitzer, Adv. Math. 5:246 (1970).
H. K. Janssen and B. Schmittmann, Z. Phys. B 64:503 (1986); K.-t. Leung and J. L. Cardy, J. Stat. Phys. 44:567 (1986) and 45:1087 (1986).
C. C. Hill, R. K. P. Zia, and B. Schmittmann, Phys. Rev. Lett. 77:514 (1996).
R. Dickman, Phys. Rev. B 38:2588 (1988), and N. C. Pesheva, Y. Shnidman, and R. K. P. Zia, J. Stat. Phys. 70:737 (1993).
L. B. Shaw, B. Schmittmann, and R. K. P. Zia, to be published.
N. Metropolis, A. W. Rosenbluth, M. M. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21:1087 (1953).
K. Hwang, B. Schmittmann, and R. K. P. Zia, Phys. Rev. Lett. 67:326 (1991) and Phys. Rev. E 48:800 (1993).
K.-t. Leung, Phys. Rev. Lett. 66:453 (1991) and Int. J. Mod. Phys. C 3:367 (1992); J.-S. Wang, J. Stat. Phys. 82:1409 (1996).
J. Marro, J. L. Lebowitz, H. Spohn, and M. H. Kalos, J. Stat. Phys. 38:725 (1985).
M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions (Washington, 1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schmittmann, B., Zia, R.K.P. Two-Point Correlations and Critical Line of the Driven Ising Lattice Gas in a High-Temperature Expansion. Journal of Statistical Physics 91, 525–539 (1998). https://doi.org/10.1023/A:1023069325518
Issue Date:
DOI: https://doi.org/10.1023/A:1023069325518