Abstract
An Ising model in the lattice gas representation is driven far from equilibrium by an external ‘electric’ field. In steady state, a current prevails. The usual second order phase transition persists, but with non-Ising critical singularities. In this article, we concentrate on singularities of correlations which exist for all temperatures away from criticality. A consequence of the violation of the fluctuation-dissipation theorem in non-equilibrium systems, these generic features are studied both analytically and via simulation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Katz, J.L. Lebowitz, and H. Spohn, Phys. Rev. B28, 1655 (1983) and
1.a 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 (986) and
J.L. Vallés and J. Marro, J. Stat. Phys. 49, 89 (1987);
J. Marro and J.L. Vallés, J. Stat. Phys. 49, 121 (1987);
and J. Marro, J.L. Vallés and J.M. Gonzalez-Miranda, Phys. Rev. B35, 3372 (1987).
H. K. Janssen and B. Schmittmann, Z. Phys. B63, 517 (1986),
K.-t. Leung and J.L. Cardy, J. Stat. Phys. 44, 567 (1986)
and K. Gawedzki and A. Kupiainen, Nucl. Phys. B269, 45 (1986).
B. Schmittmann, Int. J. Mod. Phys. B4 2269 (1990).
K. Kawasaki, in Phase Transitions and Critical Phenomena, ed. C. Domb and M. S. Green (Academic, N. Y., 1972) Vol. 2.
N. Metropolis, A.W. Rosenbluth, M.M. Rosenbluth, A.H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).
J.L. Vallés, K.-t. Leung and R. K. P. Zia, in Computer Simulation Studies in Condensed Matter Physics II, eds. D.P. Landau, K.K. Mon and H.-B. Schüttler, (Springer-Verlag, Berlin, 1990) pp. 152.
See, e.g., D. J. Amit, Field Theory, the Renormalization Group, and Critical Phenomena (2nd edition: World Scientific, Singapore 1984).
B.I. Halperin, P. C. Hohenberg and S-K. Ma, Phys. Rev., B10, 139 (1974).
For a review, see P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys., 49, 435 (1977).
R. Kubo, Rep. Progr. Phys., 29, 255 (1966).
B. Schmittmann and R.K.P. Zia, to be published in Phase Transitions and Critical Phenomena, eds. C. Domb and J.L. Lebowitz, (Academic, N.Y.)
K.-t. Leung, Phys. Rev. Lett. 66, 453 (1991).
M.Q. Zhang, J.-S. Wang, J.L. Lebowitz and J.L. Vallés, J. Stat. Phys. 52, 1461 (1988).
P.L. Garrido, J.L. Lebowitz, C. Maes and H. Spohn, Phys. Rev. A42, 1954 (1990).
G. Grinstein, J. Appi. Phys. 69, 5441 (1991).
K. Hwang, B. Schmittmann and R.K.P. Zia, Phys. Rev. Lett. 67, 326 (1991).
D.J. Wallace and R.K.P. Zia, Phys. Rev. Lett. 43, 808 (1979).
F.P. Buff, R.A. Lovett and F.H. Stillinger, Phys. Rev. Lett. 15, 621(1965).
For a review and references, see R.K.P. Zia, in Progress in Statistical Mechanics, ed. CK. Hu, (World Scientific, Singapore, 1988) pp. 303.
H. van Beijeren and I Nolden, in Topics in Current Physics, ed. W. Schommers and P. von Blanckenhagen (Springer-Verlag, Berlin, 1987) Vol.43.
H.W. Diehl, D.M. Kroll and H. Wagner, Z. Physik B36, 329 (1980);
S.C. Lin and M.J. Lowe, J. Phys. A16, 347 (1983)
and R.K.P. Zia, Nucl. Phys., B251, 676 (1985).
K.-t. Leung, K.K. Mon, J.L. Vallés and R.K.P. Zia, Phys. Rev. Lett. 61, 1744 (1988) and
K.-t. Leung, K.K. Mon, J.L. Vallés and R.K.P. Zia, Phys. Rev. B39, 9312 (1989).
See, for example, K.K. Mon, S. Wansleben, D.P. Landau and K. Binder, Phys. Rev. Lett. 60, 708 (1988)
and K.K. Mon, S. Wansleben, D.P. Landau and K. Binder Phys. Rev. B39, 7089 (1989).
J.L. Vallés, K.-t. Leung and R.K.P. Zia, J. Stat. Phys. 56, 43 (1989).
R.K.P. Zia and K.-t. Leung, J. Phys. A24, L1399 (1991).
B. Schmittmann and R.K.P. Zia, Phys. Rev. Lett. 66, 357 (1991).
A. Onuki and K. Kawasaki, Ann.Phys. 121, 456(1979)and
A. Onuki and K. Kawasaki, Ann.Phys. 131, 217(1981);
D. Beysens and M. Gbadamassi, Phys. Rev. A22, 2250 (1980);
D. Ronis and I. Procaccia, Phys. Rev. A25, 1812 (1982);
A.-M.S. Trembley, E.D. Siggia and M.R. Arai, Phys. Rev. A23, 1451 (1981)and
A.-M.S. Trembley, E.D. Siggia and M.R. Arai, Phys. Rev. A24, 1655 (1981);
J.W. Duffy and J. Lutsko, in Recent Developments in Nonequilibrium Thermodynamics, eds. J. Casas-Vazques, D. Jou and J.M. Rubi, (Spinger, Berlin, 1986);
CK. Chan and L. Lin, Europhys. Lett. 11, 13 (1990).
D. Ronis, I. Procaccia and I. Oppenheim, Phys. Rev. A19, 1324 (1979);
R. Desai and M. Grant, Phys Rev A27, 2577 (1981);
T.R. Kirkpatrick, E.G.D. Cohen and J.R. Dorfman, Phys. Rev. A26, 950 (1982);
R. Schmitz, Phys. Rep. 171, 1 (1988);
and B.M. Law and J.V. Sengers, J. Stat. Phys. 57, 531 (1989).
R.P. Smith, Acta Metal. 1, 578 (1953);
G.E. Murch, Phil. Mag. A41, 157 (1980);
H. Spohn, J. Phys. A16, 4275 (1983);
J.V. Andersen and O.G. Mouritsen, Phys. Rev. Lett. 65, 440 (1990);
and J. Krug, Phys. Rev. Lett. 67, 1882 (1990).
P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. A38, 364 (1988).
J.M. Carlson and J.S. Langer, Phys. Rev. Lett. 62, 2632 (1989).
R.K.P. Zia and K.-t. Leung, to be published.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zia, R.K.P., Hwang, K., Leung, Kt., Schmittmann, B. (1993). Generically Singular Correlations in a Non-Equilibrium Steady-State System. In: Landau, D.P., Mon, K.K., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics V. Springer Proceedings in Physics, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78083-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-78083-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-78085-1
Online ISBN: 978-3-642-78083-7
eBook Packages: Springer Book Archive