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Finite-size scaling and universality for the totally asymmetric simple-exclusion process

Jordan Brankov* and Nadezhda Bunzarova

  • Institute of Mechanics, Bulgarian Academy of Sciences, Academician G. Bonchev Street 4, 1113 Sofia, Bulgaria

  • *Electronic address: brankov@bas.bg
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Phys. Rev. E 71, 036130 – Published 22 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.036130

Abstract

The applicability of the concepts of finite-size scaling and universality to nonequilibrium phase transitions is considered in the framework of the one-dimensional totally asymmetric simple-exclusion process with open boundaries. In the thermodynamic limit there are boundary-induced transitions both of the first and second order between steady-state phases of the model. We derive finite-size scaling expressions for the current near the continuous phase transition and for the local density near the first-order transition under different stochastic dynamics and compare them to establish the existence of universal functions. Next we study numerically the finite-size behavior of the Lee-Yang zeros of the normalization factor for the different steady-state probabilities.

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References (56)

  1. M. E. Fisher, in Critical Phenomena, Proceedings of the Enrico Fermi International School of Physics, edited by M. S. Green (Academic Press, New York, 1971), Vol. 51.
  2. M. E. Fisher and M. N. Barber, Phys. Rev. Lett. 28, 1516 (1972).
  3. M. N. Barber, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, London, 1983), Vol. 8.
  4. V. Privman, P. C. Hohenberg, and A. Aharony, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, London, 1991), Vol. 14.
  5. J. G. Brankov, D. M. Danchev, and N. S. Tonchev, Theory of Critical Phenomena in Finite-Size Systems. Scaling and Quantum Effects (World Scientific, Singapore, 2000).
  6. C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952).
  7. M. E. Fisher, in Lectures in Theoretical Physics, edited by W. E. Brittin (University of Colorado Press, Boulder, 1965), Vol. 7C.
  8. B. Derrida, J. L. Lebowitz, and E. R. Speer, Phys. Rev. Lett. 87, 150601 (2001).
  9. B. Derrida, J. L. Lebowitz, and E. R. Speer, Phys. Rev. Lett. 89, 030601 (2002).
  10. M. Henkel and H. Hinrichsen, J. Phys. A 37, R117 (2004).
  11. J. Brankov, Phys. Rev. E 65, 046111 (2002).
  12. C. T. MacDonald, J. H. Gibbs, and A. C. Pipkin, Biopolymers 6, 1 (1968).
  13. G. Schönherr and G. M. Schütz, J. Phys. A 37, 8215 (2004).
  14. K. Nagel and M. Schreckenberg, J. Phys. I 2, 2221 (1992).
  15. T. Antal and M. G. M. Schütz, Phys. Rev. E 62, 83 (2000).
  16. R. Barlovic, T. Huisinga, A. Schadschneider, and M. Schreckenberg, Phys. Rev. E 66, 046113 (2002).
  17. T. Huisinga, R. Barlovic, W. Knospe, A. Schadschneider, and M. Schreckenberg, Physica A 294, 249 (2001).
  18. L. H. Gwa and H. Spohn, Phys. Rev. Lett. 68, 725 (1992).
  19. S. A. Janovsky and J. L. Lebowitz, Phys. Rev. A 45, 618 (1992).
  20. F. H. Jafarpour, Physica A 339, 369 (2004).
  21. R. Lipowsky, S. Klumpp, and T. M. Nieuwenhuizen, Phys. Rev. Lett. 87, 108101 (2001).
  22. A. Parmeggiani, T. Franosch, and E. Frey, Phys. Rev. Lett. 90, 086601 (2003).
  23. R. Bundschuh, Phys. Rev. E 65, 031911 (2002).
  24. B. Derrida, Phys. Rep. 301, 65 (1998).
  25. G. M. Schütz, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, London, 2001), Vol. 19.
  26. P. F. Arndt, Phys. Rev. Lett. 84, 814 (2000).
  27. P. F. Arndt, S. R. Dahmen, and H. Hindrichsen, Physica A 259, 128 (2001).
  28. S. M. Dammer, S. R. Dahmen, and H. Hindrichsen, J. Phys. A 35, 4527 (2002).
  29. R. A. Blythe and M. R. Evans, Phys. Rev. Lett. 89, 080601 (2002).
  30. R. A. Blythe and M. R. Evans, Braz. J. Phys. 33, 464 (2003).
  31. I. Bena, F. Coppex, M. Droz, and A. Lipowski, Phys. Rev. Lett. 91, 160602 (2003).
  32. F. H. Jafarpour, J. Stat. Phys. 113, 269 (2003).
  33. F. H. Jafarpour, J. Phys. A 36, 7497 (2003).
  34. R. A. Blythe, W. Janke, D. A. Johnston, and R. Kenna, J. Stat. Mech.: Theory Exp. 2004 P06001 (2004).
  35. R. A. Blythe, W. Janke, D. A. Johnston, and R. Kenna, J. Stat. Mech.: Theory Exp. 2004 P10007 (2004).
  36. R. Brak and J. W. Essam, J. Phys. A 37, 4183 (2004).
  37. R. Brak, J. de Gier, and V. Rittenberg, J. Phys. A 37, 4303 (2004).
  38. T. M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (Springer-Verlag, Berlin, 1999).
  39. N. Rajewsky, L. Santen, A. Schadschneider, and M. Schreckenberg, J. Stat. Phys. 92, 151 (1998).
  40. D. Derrida, E. Domany, and D. Mukamel, J. Stat. Phys. 69, 667 (1992).
  41. G. Schütz and E. Domany, J. Stat. Phys. 72, 277 (1993).
  42. B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, J. Phys. A 26, 1493 (1993).
  43. N. Rajewsky, A. Schadschneider, and M. Schreckenberg, J. Phys. A 29, L305 (1996).
  44. A. Honecker and I. Peschel, J. Stat. Phys. 88, 319 (1997).
  45. J. Brankov, N. Pesheva, and N. Valkov, Phys. Rev. E 61, 2300 (2000).
  46. H. Hinrichsen, J. Phys. A 29, 3659 (1996).
  47. N. Rajewsky and M. Schreckenberg, Physica A 245, 139 (1997).
  48. M. R. Evans, N. Rajewsky, and E. R. Speer, J. Stat. Phys. 95, 45 (1999).
  49. J. de Gier and B. Nienhuis, Phys. Rev. E 59, 4899 (1999).
  50. V. Privman and M. E. Fisher, Phys. Rev. B 30, 322 (1984).
  51. H. Hinrichsen, Adv. Phys. 49, 815 (2000).
  52. M. Henkel and U. Schollwöck, J. Phys. A 39, 3333 (2001).
  53. M. Henkel and H. Hinrichsen, J. Phys. A 34, 1561 (2001).
  54. J. Brankov and N. Pesheva, Phys. Rev. E 63, 046111 (2001).
  55. R. Brak, J. W. Essam, and A. L. Owczarek, J. Stat. Phys. 93, 155 (1998).
  56. M. Uchiyama, T. Sasamoto, and M. Wadati, J. Phys. A 37, 4985 (2004).

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Phys. Rev. E 71, 036130– Published 22 March, 2005
  • Received 22 October 2004

© 2005 American Physical Society

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