Abstract
The Ising lattice gas, with its well known equilibrium properties, displays a number of surprising phenomena when driven into nonequilibrium steady states. We study such a model with anisotropic interparticle interactions (J ||≠J ⊥), using both Monte Carlo simulations and high temperature series techniques. Under saturation drive, the shift in the transition temperature can be both positive and negative, depending on the ratio J ||/J ⊥! For finite drives, both first- and second-order transitions are observed. Some aspects of the phase diagram can be predicted by investigating the two-point correlation function at the first nontrivial order of a high-temperature series expansion.
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REFERENCES
S. Katz, J. L. Lebowitz, and H. Spohn, Phys. Rev. B 28:1655 (1983) and J. Stat. Phys. 34:497 (1984).
E. Ising, Z. Physic 31:253 (1925).
For a recent review of driven systems see, for example, B. Schmittmann and R. K. P. Zia, in Phase Transitions and Critical Phenomena, Vol. 17, C. Domb and J. L. Lebowitz, eds. (Academic, London, 1995).
K.-t. Leung, Phys. Rev. Lett. 66:453 (1991) and I. J. Mod. Phys. C3:367 (1992). See also J. S. Wang, J. Stat. Phys. 82:1409 (1996).
C. C. Hill, R. K. P. Zia, and B. Schmittmann, Phys. Rev. Lett. 77:514 (1996) and C. C. Hill, Senior Thesis, Virginia Polytechnic Institute and State University (1996).
J. L. Vallés, K.-t. Leung, and R. K. P. Zia, J. Stat. Phys. 56:43 (1989); D. H. Boal, B. Schmittmann, and R. K. P. Zia, Phys. Rev. A 43:5214 (1991).
A. Achahbar and J. Marro, J. Stat. Phys. 78:1493 (1995).
H. van Beijeren and L. S. Schulman, Phys. Rev. Lett. 53:806 (1984); J. Krug, J. L. Lebowitz, H. Spohn, and M. Q. Zhang, J. Stat. Phys. 44:535 (1986).
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).
B. Schmittmann and R. K. P. Zia, J. Stat. Phys. 91:525 (1998).
L. Onsager, Phys. Rev. 65:117 (1944) and Nuovo Cim. 6 (Suppl.), 261 (1949).
C. N. Yang and T. D. Lee, Phys. Rev. 87:404 (1952); and T. D. Lee and C. N. Yang, Phys. Rev. 87:410 (1952).
B. McCoy and T. T. Wu, The Two-Dimensional Ising Model (Harvard Univ. Press, Cambridge, MA, 1973).
H. A. Kramers and G. K. Wannier, Phys. Rev. 60:252 (1941).
K. Kawasaki, Phys. Rev. 148:375 (1966) and in Phase Transitions and Critical Phenomena, Vol. 2, C. Domb and M. S. Green, eds. (Academic, New York, 1972).
N. Metropolis, A. W. Rosenbluth, M. M. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21:1087 (1953).
L. B. Shaw, B. Schmittmann, and R. K. P. Zia, to be published.
M. S. Rudzinsky and R. K. P. Zia, J. Phys. A 29:6717 (1996).
Onsager first computed these energies.(11) For a more recent review, see, e.g., R. K. P. Zia, in Statistical and Particle Physics: Common Problems and Techniques, K. C. Bowler and A. J. McKane, eds. (SUSSP Publications, Edinburgh, 1984).
M. E. Fisher and A. E. Ferdinand, Phys. Rev. Lett. 19:169 (1967); R. K. P. Zia, Phys. Lett. 64A:345 (1978).
N. C. Pesheva, Y. Shnidman, and R. K. P. Zia, J. Stat. Phys. 70:737 (1993); YS etc.
R. K. P. Zia, K. Hwang, B. Schmittmann, and K.-t. Leung, Physica A 194:183 (1993).
H. K. Janssen and B. Schmittmann, Z. Phys. B 64:503 (1986); K.-t. Leung and J. L. Cardy, J. Stat. Phys. 44:567 and 45:1087 (1986).
K. E. Bassler and Z. Racz, Phys. Rev. Lett. 73:1320 (1994).
K. E. Bassler and R. K. P. Zia, J. Stat. Phys. 80:499 (1995).
M. E. Fisher, in Critical Phenomena, M. S. Green, ed., International School of Physics “Enrico Fermi, ” Course 51 (Academic, New York, 1971). For applications to driven systems, see K.-t. Leung, Int. J. Mod. Phys. C 3:367 (1992).
R. K. P. Zia and K.-t. Leung, J. Phys. A 24:L1399 (1991); K.-t. Leung and R. K. P. Zia, J. Phys. A 26:L737 (1993).
W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 34:323 (1963) and 35:444 (1964).
K.-t. Leung, J. Stat. Phys. 50:405 (1988) and 61:341 (1990).
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Shaw, L.B., Schmittmann, B. & Zia, R.K.P. Phase Transitions in a Driven Lattice Gas with Anisotropic Interactions. Journal of Statistical Physics 95, 981–996 (1999). https://doi.org/10.1023/A:1004554517737
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DOI: https://doi.org/10.1023/A:1004554517737