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Nonequilibrium phase transitions into absorbing states

Focused around the pair contact process with diffusion

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Abstract

Systems with absorbing (trapped) states may exhibit a nonequilibrium phase transition from a noise-free inactive phase into an ever-lasting active phase. We briefly review the absorbing critical phenomena and universality classes, and discuss over the controversial issues on the pair contact process with diffusion (PCPD). Two different approaches are proposed to clarify its universality issue, which unveil strong evidences that the PCPD belongs to a new universality class other than the directed percolation class.

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References

  1. J. Marro, R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999)

    Google Scholar 

  2. H. Hinrichsen, Adv. Phys. 49, 815 (2000)

    Article  ADS  Google Scholar 

  3. G. Ódor, Rev. Mod. Phys. 76, 663 (2004)

    Article  ADS  Google Scholar 

  4. S. Lübeck, Int. J. Mod. Phys. B 18, 3977 (2004)

    Article  ADS  Google Scholar 

  5. N.G. van Kampen, Stochastic processes in physics and chemistry, 2nd edn. (North Holland, Amsterdam, 1997)

    Google Scholar 

  6. P. Grassberger, A. de la Torre, Ann. Phys. (NY) 122, 373 (1979)

    Article  ADS  Google Scholar 

  7. T.E. Harris, Ann. Prob. 2, 969 (1974)

    Article  MATH  Google Scholar 

  8. H.-K. Janssen, Z. Phys. B: Condens. Matter 42, 151 (1981)

    Article  ADS  Google Scholar 

  9. P. Grassberger, Z. Phys. B: Condens. Matter 47, 365 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  10. G. Grinstein, Z.-W. Lai, D.A. Browne, Phys. Rev. A 40, 4820 (1989)

    Article  ADS  Google Scholar 

  11. I. Jensen, Phys. Rev. Lett. 70, 1465 (1993)

    Article  ADS  Google Scholar 

  12. M.A. Muñoz, G. Grinstein, R. Dickman, J. Stat. Phys. 91, 541 (1998)

    Article  MATH  Google Scholar 

  13. A. Jiménez-Dalmaroni, H. Hinrichsen, Phys. Rev. E 68, 036103 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  14. R. Dickman, Phys. Rev. E 53, 2223 (1996)

    Article  ADS  Google Scholar 

  15. P. Grassberger, H. Chaté, G. Rousseau, Phys. Rev. E 55, 2488 (1997)

    Article  ADS  Google Scholar 

  16. M.H. Kim, H. Park, Phys. Rev. Lett. 73, 2579 (1994)

    Article  ADS  Google Scholar 

  17. H. Park, M.H. Kim, H. Park, Phys. Rev. E 52, 5664 (1995)

    Article  ADS  Google Scholar 

  18. W. Hwang, S. Kwon, H. Park, H. Park, Phys. Rev. E 57, 6438 (1998)

    Article  ADS  Google Scholar 

  19. W. Hwang, H. Park, Phys. Rev. E 59, 4683 (1999)

    Article  ADS  Google Scholar 

  20. M.C. Marques, J.F.F. Mendes, Eur. Phys. J. B 12, 123 (1999)

    Article  ADS  Google Scholar 

  21. H.S. Park, H. Park, J. Korean Phys. Soc. 38, 494 (2001)

    Google Scholar 

  22. P. Grassberger, J. Phys. A: Math. Gen. 22, L1103 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  23. H. Takayasu, A.Y. Tretyakov, Phys. Rev. Lett. 68, 3060 (1992)

    Article  ADS  Google Scholar 

  24. O.A. Hammal, H. Chaté, I. Dornic, M.A. Muñoz, Phys. Rev. Lett. 94, 230601 (2005)

    Article  Google Scholar 

  25. H. Park, H. Park, Physica A 221, 97 (1995)

    Article  ADS  Google Scholar 

  26. S. Kwon, H. Park, Phys. Rev. E 52, 5955 (1995)

    Article  ADS  Google Scholar 

  27. K.E. Bassler, D.A. Browne, Phys. Rev. Lett. 77, 4094 (1996)

    Article  ADS  Google Scholar 

  28. H. Hinrichsen, Phys. Rev. E 55, 219 (1997)

    Article  ADS  Google Scholar 

  29. R. Kree, B. Schaub, B. Schmittmann, Phys. Rev. A 39, 2214 (1989)

    Article  ADS  Google Scholar 

  30. F. van Wijland, K. Oerding, H.J. Hilhorst, Physica A 251, 179 (1998)

    Article  Google Scholar 

  31. J.D. Noh, H. Park, Phys. Rev. E 69, 016122 (2004)

    Article  ADS  Google Scholar 

  32. R. Dickman, M.A.F. de Menezes, Phys. Rev. E 66, 045101(R) (2004)

    ADS  Google Scholar 

  33. M. Henkel, H. Hinrichsen, J. Phys. A: Math. Gen. 37, R117 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  34. S.-C. Park, H. Park, Phys. Rev. E 71, 016137 (2005)

    Article  ADS  Google Scholar 

  35. G. Ódor, M.C. Marques, M.A. Santos, Phys. Rev. E 65, 056113 (2002)

    Article  ADS  Google Scholar 

  36. G.T. Barkema, E. Carlon, Phys. Rev. E 68, 036113 (2003)

    Article  ADS  Google Scholar 

  37. H. Hinrichsen, Physica A 361, 457 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  38. E. Carlon, M. Henkel, U. Schollwöck, Phys. Rev. E 63, 036101 (2001)

    Article  ADS  Google Scholar 

  39. I. Jensen, J. Phys. A: Math. Gen. 29, 7013 (1996)

    Article  MATH  ADS  Google Scholar 

  40. H.-K. Janssens, K. Oerding, F. van Wijland, H.J. Hilhorst, Eur. Phys. J. B 7, 137 (1999)

    Article  ADS  Google Scholar 

  41. H. Hinrichsen, M. Howard, Eur. Phys. J. B 7, 635 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  42. J. Kockelkoren, H. Chaté, Phys. Rev. Lett. 90, 125701 (2003)

    Article  ADS  Google Scholar 

  43. S.-C. Park, H. Park, Phys. Rev. E 76, 051123 (2007)

    Article  ADS  Google Scholar 

  44. H.-K. Janssens, F. van Wijland, O. Deloubriere, U.C. Täuber, Phys. Rev. E 70, 056114 (2004)

    Article  ADS  Google Scholar 

  45. S.-C. Park, Eur. Phys. J. B 50, 327 (2006)

    Article  ADS  Google Scholar 

  46. M.M. de Oliveira, R. Dickman, Phys. Rev. E 74, 011124 (2006)

    Article  ADS  Google Scholar 

  47. S. Kwon, Y. Kim, Phys. Rev. E 75, 042103 (2007)

    Article  ADS  Google Scholar 

  48. J. Cardy, U.C. Täuber, Phys. Rev. Lett. 77, 4780 (1996)

    Article  ADS  Google Scholar 

  49. S.-C. Park, H. Park, Phys. Rev. Lett. 94, 065701 (2005)

    Article  ADS  Google Scholar 

  50. K. Kang, S. Redner, Phys. Rev. Lett. 52, 955 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  51. K. Kang, S. Redner, Phys. Rev. A 32, 435 (1985)

    Article  ADS  Google Scholar 

  52. D. Dhar, R. Ramaswamy, Phys. Rev. Lett. 63, 1659 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  53. S.-C. Park, H. Park, Phys. Rev. E 73, 025105 (2006)

    Article  ADS  Google Scholar 

  54. S.-C. Park, J.-M. Park, Phys. Rev. E 71, 026113 (2005)

    Article  ADS  Google Scholar 

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Correspondence to Hyunggyu Park.

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Park, SC., Park, H. Nonequilibrium phase transitions into absorbing states. Eur. Phys. J. B 64, 415–421 (2008). https://doi.org/10.1140/epjb/e2008-00022-4

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  • DOI: https://doi.org/10.1140/epjb/e2008-00022-4

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