Advertisement

Generically Singular Correlations in a Non-Equilibrium Steady-State System

  • R. K. P. Zia
  • K. Hwang
  • K.-t. Leung
  • B. Schmittmann
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 75)

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.

Keywords

Ising Model Order Phase Transition Equilibrium System Capillary Wave Goldstone Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Katz, J.L. Lebowitz, and H. Spohn, Phys. Rev. B28, 1655 (1983) andADSGoogle Scholar
  2. 1.a
    1.a S. Katz, J.L. Lebowitz, and H. Spohn, J. Stat. Phys. 34, 497 (1984).CrossRefADSMathSciNetGoogle Scholar
  3. 2.
    J. Marro, J.L. Lebowitz, H. Spohn, and M.H. Kalos, J. Stat. Phys. 38, 725 (1985);CrossRefADSGoogle Scholar
  4. 2.a
    J.L. Vallés and J. Marro, J. Stat. Phys. 43, 441 (986) andGoogle Scholar
  5. 2.b
    J.L. Vallés and J. Marro, J. Stat. Phys. 49, 89 (1987);CrossRefADSGoogle Scholar
  6. 2.c
    J. Marro and J.L. Vallés, J. Stat. Phys. 49, 121 (1987);CrossRefADSGoogle Scholar
  7. 2.d
    and J. Marro, J.L. Vallés and J.M. Gonzalez-Miranda, Phys. Rev. B35, 3372 (1987).ADSGoogle Scholar
  8. 3.
    H. K. Janssen and B. Schmittmann, Z. Phys. B63, 517 (1986),CrossRefADSGoogle Scholar
  9. 3.a
    K.-t. Leung and J.L. Cardy, J. Stat. Phys. 44, 567 (1986)CrossRefADSMathSciNetGoogle Scholar
  10. 3.b
    and K. Gawedzki and A. Kupiainen, Nucl. Phys. B269, 45 (1986).CrossRefADSMathSciNetGoogle Scholar
  11. 4.
    B. Schmittmann, Int. J. Mod. Phys. B4 2269 (1990).ADSGoogle Scholar
  12. 5.
    K. Kawasaki, in Phase Transitions and Critical Phenomena, ed. C. Domb and M. S. Green (Academic, N. Y., 1972) Vol. 2.Google Scholar
  13. 6.
    N. Metropolis, A.W. Rosenbluth, M.M. Rosenbluth, A.H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).CrossRefADSGoogle Scholar
  14. 7.
    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.CrossRefGoogle Scholar
  15. 8.
    See, e.g., D. J. Amit, Field Theory, the Renormalization Group, and Critical Phenomena (2nd edition: World Scientific, Singapore 1984).Google Scholar
  16. 9.
    B.I. Halperin, P. C. Hohenberg and S-K. Ma, Phys. Rev., B10, 139 (1974).ADSGoogle Scholar
  17. 9.a
    For a review, see P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys., 49, 435 (1977).CrossRefADSGoogle Scholar
  18. 10.
    R. Kubo, Rep. Progr. Phys., 29, 255 (1966).CrossRefADSGoogle Scholar
  19. 11.
    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.)Google Scholar
  20. 12.
    K.-t. Leung, Phys. Rev. Lett. 66, 453 (1991).CrossRefADSGoogle Scholar
  21. 13.
    M.Q. Zhang, J.-S. Wang, J.L. Lebowitz and J.L. Vallés, J. Stat. Phys. 52, 1461 (1988).CrossRefADSGoogle Scholar
  22. 14.
    P.L. Garrido, J.L. Lebowitz, C. Maes and H. Spohn, Phys. Rev. A42, 1954 (1990).ADSMathSciNetGoogle Scholar
  23. 15.
    G. Grinstein, J. Appi. Phys. 69, 5441 (1991).CrossRefADSGoogle Scholar
  24. 16.
    K. Hwang, B. Schmittmann and R.K.P. Zia, Phys. Rev. Lett. 67, 326 (1991).CrossRefADSGoogle Scholar
  25. 17.
    D.J. Wallace and R.K.P. Zia, Phys. Rev. Lett. 43, 808 (1979).CrossRefADSGoogle Scholar
  26. 18.
    F.P. Buff, R.A. Lovett and F.H. Stillinger, Phys. Rev. Lett. 15, 621(1965).CrossRefADSGoogle Scholar
  27. 19.
    For a review and references, see R.K.P. Zia, in Progress in Statistical Mechanics, ed. CK. Hu, (World Scientific, Singapore, 1988) pp. 303.Google Scholar
  28. 20.
    H. van Beijeren and I Nolden, in Topics in Current Physics, ed. W. Schommers and P. von Blanckenhagen (Springer-Verlag, Berlin, 1987) Vol.43.Google Scholar
  29. 21.
    H.W. Diehl, D.M. Kroll and H. Wagner, Z. Physik B36, 329 (1980);ADSGoogle Scholar
  30. 21.a
    S.C. Lin and M.J. Lowe, J. Phys. A16, 347 (1983)ADSGoogle Scholar
  31. 21.b
    and R.K.P. Zia, Nucl. Phys., B251, 676 (1985).CrossRefADSGoogle Scholar
  32. 22.
    K.-t. Leung, K.K. Mon, J.L. Vallés and R.K.P. Zia, Phys. Rev. Lett. 61, 1744 (1988) andCrossRefADSGoogle Scholar
  33. 22.a
    K.-t. Leung, K.K. Mon, J.L. Vallés and R.K.P. Zia, Phys. Rev. B39, 9312 (1989).ADSGoogle Scholar
  34. 23.
    See, for example, K.K. Mon, S. Wansleben, D.P. Landau and K. Binder, Phys. Rev. Lett. 60, 708 (1988)CrossRefADSGoogle Scholar
  35. 23.a
    and K.K. Mon, S. Wansleben, D.P. Landau and K. Binder Phys. Rev. B39, 7089 (1989).ADSGoogle Scholar
  36. 24.
    J.L. Vallés, K.-t. Leung and R.K.P. Zia, J. Stat. Phys. 56, 43 (1989).CrossRefADSGoogle Scholar
  37. 25.
    R.K.P. Zia and K.-t. Leung, J. Phys. A24, L1399 (1991).ADSGoogle Scholar
  38. 26.
    B. Schmittmann and R.K.P. Zia, Phys. Rev. Lett. 66, 357 (1991).CrossRefADSGoogle Scholar
  39. 27.
    A. Onuki and K. Kawasaki, Ann.Phys. 121, 456(1979)andCrossRefMATHADSGoogle Scholar
  40. 27.a
    A. Onuki and K. Kawasaki, Ann.Phys. 131, 217(1981);CrossRefADSGoogle Scholar
  41. 27.b
    D. Beysens and M. Gbadamassi, Phys. Rev. A22, 2250 (1980);ADSGoogle Scholar
  42. 27.c
    D. Ronis and I. Procaccia, Phys. Rev. A25, 1812 (1982);ADSGoogle Scholar
  43. 27.d
    A.-M.S. Trembley, E.D. Siggia and M.R. Arai, Phys. Rev. A23, 1451 (1981)andADSGoogle Scholar
  44. 27.e
    A.-M.S. Trembley, E.D. Siggia and M.R. Arai, Phys. Rev. A24, 1655 (1981);ADSGoogle Scholar
  45. 27.f
    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);Google Scholar
  46. 27.g
    CK. Chan and L. Lin, Europhys. Lett. 11, 13 (1990).CrossRefADSGoogle Scholar
  47. 28.
    D. Ronis, I. Procaccia and I. Oppenheim, Phys. Rev. A19, 1324 (1979);ADSGoogle Scholar
  48. 28.a
    R. Desai and M. Grant, Phys Rev A27, 2577 (1981);Google Scholar
  49. 28.b
    T.R. Kirkpatrick, E.G.D. Cohen and J.R. Dorfman, Phys. Rev. A26, 950 (1982);ADSGoogle Scholar
  50. 28.c
    R. Schmitz, Phys. Rep. 171, 1 (1988);CrossRefADSGoogle Scholar
  51. 28.d
    and B.M. Law and J.V. Sengers, J. Stat. Phys. 57, 531 (1989).CrossRefADSGoogle Scholar
  52. 29.
    R.P. Smith, Acta Metal. 1, 578 (1953);CrossRefGoogle Scholar
  53. 29.a
    G.E. Murch, Phil. Mag. A41, 157 (1980);ADSGoogle Scholar
  54. 29.b
    H. Spohn, J. Phys. A16, 4275 (1983);ADSMathSciNetGoogle Scholar
  55. 29.c
    J.V. Andersen and O.G. Mouritsen, Phys. Rev. Lett. 65, 440 (1990);CrossRefADSGoogle Scholar
  56. 29.d
    and J. Krug, Phys. Rev. Lett. 67, 1882 (1990).CrossRefADSGoogle Scholar
  57. 30.
    P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. A38, 364 (1988).ADSMathSciNetGoogle Scholar
  58. 31.
    J.M. Carlson and J.S. Langer, Phys. Rev. Lett. 62, 2632 (1989).CrossRefADSGoogle Scholar
  59. 32.
    R.K.P. Zia and K.-t. Leung, to be published.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • R. K. P. Zia
    • 1
  • K. Hwang
    • 1
  • K.-t. Leung
    • 1
  • B. Schmittmann
    • 1
  1. 1.Center for Stochastic Processes in Science and Engineering and Physics DepartmentVirginia Polytechnic Institute and State UniversityBlacksburgUSA

Personalised recommendations