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

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Computer Simulation Studies in Condensed-Matter Physics V

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 75))

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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.

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References

  1. S. Katz, J.L. Lebowitz, and H. Spohn, Phys. Rev. B28, 1655 (1983) and

    ADS  Google Scholar 

  2. 1.a S. Katz, J.L. Lebowitz, and H. Spohn, J. Stat. Phys. 34, 497 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  3. J. Marro, J.L. Lebowitz, H. Spohn, and M.H. Kalos, J. Stat. Phys. 38, 725 (1985);

    Article  ADS  Google Scholar 

  4. J.L. Vallés and J. Marro, J. Stat. Phys. 43, 441 (986) and

    Google Scholar 

  5. J.L. Vallés and J. Marro, J. Stat. Phys. 49, 89 (1987);

    Article  ADS  Google Scholar 

  6. J. Marro and J.L. Vallés, J. Stat. Phys. 49, 121 (1987);

    Article  ADS  Google Scholar 

  7. and J. Marro, J.L. Vallés and J.M. Gonzalez-Miranda, Phys. Rev. B35, 3372 (1987).

    ADS  Google Scholar 

  8. H. K. Janssen and B. Schmittmann, Z. Phys. B63, 517 (1986),

    Article  ADS  Google Scholar 

  9. K.-t. Leung and J.L. Cardy, J. Stat. Phys. 44, 567 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  10. and K. Gawedzki and A. Kupiainen, Nucl. Phys. B269, 45 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  11. B. Schmittmann, Int. J. Mod. Phys. B4 2269 (1990).

    ADS  Google Scholar 

  12. K. Kawasaki, in Phase Transitions and Critical Phenomena, ed. C. Domb and M. S. Green (Academic, N. Y., 1972) Vol. 2.

    Google Scholar 

  13. N. Metropolis, A.W. Rosenbluth, M.M. Rosenbluth, A.H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).

    Article  ADS  Google Scholar 

  14. 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.

    Chapter  Google Scholar 

  15. See, e.g., D. J. Amit, Field Theory, the Renormalization Group, and Critical Phenomena (2nd edition: World Scientific, Singapore 1984).

    Google Scholar 

  16. B.I. Halperin, P. C. Hohenberg and S-K. Ma, Phys. Rev., B10, 139 (1974).

    ADS  Google Scholar 

  17. For a review, see P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys., 49, 435 (1977).

    Article  ADS  Google Scholar 

  18. R. Kubo, Rep. Progr. Phys., 29, 255 (1966).

    Article  ADS  Google Scholar 

  19. 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. K.-t. Leung, Phys. Rev. Lett. 66, 453 (1991).

    Article  ADS  Google Scholar 

  21. M.Q. Zhang, J.-S. Wang, J.L. Lebowitz and J.L. Vallés, J. Stat. Phys. 52, 1461 (1988).

    Article  ADS  Google Scholar 

  22. P.L. Garrido, J.L. Lebowitz, C. Maes and H. Spohn, Phys. Rev. A42, 1954 (1990).

    ADS  MathSciNet  Google Scholar 

  23. G. Grinstein, J. Appi. Phys. 69, 5441 (1991).

    Article  ADS  Google Scholar 

  24. K. Hwang, B. Schmittmann and R.K.P. Zia, Phys. Rev. Lett. 67, 326 (1991).

    Article  ADS  Google Scholar 

  25. D.J. Wallace and R.K.P. Zia, Phys. Rev. Lett. 43, 808 (1979).

    Article  ADS  Google Scholar 

  26. F.P. Buff, R.A. Lovett and F.H. Stillinger, Phys. Rev. Lett. 15, 621(1965).

    Article  ADS  Google Scholar 

  27. 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. 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. H.W. Diehl, D.M. Kroll and H. Wagner, Z. Physik B36, 329 (1980);

    ADS  Google Scholar 

  30. S.C. Lin and M.J. Lowe, J. Phys. A16, 347 (1983)

    ADS  Google Scholar 

  31. and R.K.P. Zia, Nucl. Phys., B251, 676 (1985).

    Article  ADS  Google Scholar 

  32. K.-t. Leung, K.K. Mon, J.L. Vallés and R.K.P. Zia, Phys. Rev. Lett. 61, 1744 (1988) and

    Article  ADS  Google Scholar 

  33. K.-t. Leung, K.K. Mon, J.L. Vallés and R.K.P. Zia, Phys. Rev. B39, 9312 (1989).

    ADS  Google Scholar 

  34. See, for example, K.K. Mon, S. Wansleben, D.P. Landau and K. Binder, Phys. Rev. Lett. 60, 708 (1988)

    Article  ADS  Google Scholar 

  35. and K.K. Mon, S. Wansleben, D.P. Landau and K. Binder Phys. Rev. B39, 7089 (1989).

    ADS  Google Scholar 

  36. J.L. Vallés, K.-t. Leung and R.K.P. Zia, J. Stat. Phys. 56, 43 (1989).

    Article  ADS  Google Scholar 

  37. R.K.P. Zia and K.-t. Leung, J. Phys. A24, L1399 (1991).

    ADS  Google Scholar 

  38. B. Schmittmann and R.K.P. Zia, Phys. Rev. Lett. 66, 357 (1991).

    Article  ADS  Google Scholar 

  39. A. Onuki and K. Kawasaki, Ann.Phys. 121, 456(1979)and

    Article  MATH  ADS  Google Scholar 

  40. A. Onuki and K. Kawasaki, Ann.Phys. 131, 217(1981);

    Article  ADS  Google Scholar 

  41. D. Beysens and M. Gbadamassi, Phys. Rev. A22, 2250 (1980);

    ADS  Google Scholar 

  42. D. Ronis and I. Procaccia, Phys. Rev. A25, 1812 (1982);

    ADS  Google Scholar 

  43. A.-M.S. Trembley, E.D. Siggia and M.R. Arai, Phys. Rev. A23, 1451 (1981)and

    ADS  Google Scholar 

  44. A.-M.S. Trembley, E.D. Siggia and M.R. Arai, Phys. Rev. A24, 1655 (1981);

    ADS  Google Scholar 

  45. 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. CK. Chan and L. Lin, Europhys. Lett. 11, 13 (1990).

    Article  ADS  Google Scholar 

  47. D. Ronis, I. Procaccia and I. Oppenheim, Phys. Rev. A19, 1324 (1979);

    ADS  Google Scholar 

  48. R. Desai and M. Grant, Phys Rev A27, 2577 (1981);

    Google Scholar 

  49. T.R. Kirkpatrick, E.G.D. Cohen and J.R. Dorfman, Phys. Rev. A26, 950 (1982);

    ADS  Google Scholar 

  50. R. Schmitz, Phys. Rep. 171, 1 (1988);

    Article  ADS  Google Scholar 

  51. and B.M. Law and J.V. Sengers, J. Stat. Phys. 57, 531 (1989).

    Article  ADS  Google Scholar 

  52. R.P. Smith, Acta Metal. 1, 578 (1953);

    Article  Google Scholar 

  53. G.E. Murch, Phil. Mag. A41, 157 (1980);

    ADS  Google Scholar 

  54. H. Spohn, J. Phys. A16, 4275 (1983);

    ADS  MathSciNet  Google Scholar 

  55. J.V. Andersen and O.G. Mouritsen, Phys. Rev. Lett. 65, 440 (1990);

    Article  ADS  Google Scholar 

  56. and J. Krug, Phys. Rev. Lett. 67, 1882 (1990).

    Article  ADS  Google Scholar 

  57. P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. A38, 364 (1988).

    ADS  MathSciNet  Google Scholar 

  58. J.M. Carlson and J.S. Langer, Phys. Rev. Lett. 62, 2632 (1989).

    Article  ADS  Google Scholar 

  59. R.K.P. Zia and K.-t. Leung, to be published.

    Google Scholar 

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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

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  • DOI: https://doi.org/10.1007/978-3-642-78083-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

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