Journal of Statistical Physics

, Volume 129, Issue 3, pp 593–603 | Cite as

Phase Transition between Synchronous and Asynchronous Updating Algorithms

  • Filippo Radicchi
  • Daniele Vilone
  • Hildegard Meyer-Ortmanns
Article

Abstract

We update a one-dimensional chain of Ising spins of length L with algorithms which are parameterized by the probability p for a certain site to get updated in one time step. The result of the update event itself is determined by the energy change due to the local change in the configuration. In this way we interpolate between the Metropolis algorithm at zero temperature when p is of the order of 1/L and L is large, and a synchronous deterministic updating procedure for p=1. As a function of p we observe a phase transition between the stationary states to which the algorithm drives the system. These are non-absorbing stationary states with antiferromagnetic domains for p>p c , and absorbing states with ferromagnetic domains for pp c . This means that above this transition the stationary states have lost any remnants of the ferromagnetic Ising interaction. A measurement of the critical exponents shows that this transition belongs to the universality class of parity conservation.

Keywords

Nonequilibrium and irreversible dynamics Phase transitions 

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References

  1. 1.
    Klemm, K., Bornholdt, S.: Pre-print, arXiv:q-bio/0309013 (2003) Google Scholar
  2. 2.
    Greil, F., Drossel, B.: Phys. Rev. Lett. 95, 048701 (2005) CrossRefADSGoogle Scholar
  3. 3.
    Hopfield, J.J.: Proc. Nat. Acad. Sci. USA 79, 2554 (1982) CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Grondin, R.O., Porod, W., Loeffler, C.M., Ferry, D.K.: Biol. Cybern. 49, 1 (1983) MATHCrossRefGoogle Scholar
  5. 5.
    Klemm, K., Bornholdt, S.: Proc. Nat. Acad. Sci. USA 102, 18414 (2005) CrossRefADSGoogle Scholar
  6. 6.
    Klemm, K., Bornholdt, S.: Phys. Rev. E 72, 055101 (2005) CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Huberman, B.A., Glance, N.S.: Proc. Nat. Acad. Sci. USA 90, 7716 (1993) MATHCrossRefADSGoogle Scholar
  8. 8.
    Block, H.J., Bergersen, B.: Phys. Rev. E 59, 3876 (1999) CrossRefADSGoogle Scholar
  9. 9.
    Arjomandi, E., Fischer, M.J., Lynch, N.A.: J. ACM 30, 449 (1983) MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Newman, M.E.J., Barkema, G.T.: Monte Carlo Methods in Statistical Physics. Oxford University Press, Oxford (1999) MATHGoogle Scholar
  11. 11.
    Metropolis, N.A., Rosenbluth, M.N., Rosenbluth, A.H., Teller, E., Teller, J.: J. Chem. Phys. 21, 1087 (1953) CrossRefADSGoogle Scholar
  12. 12.
    Samuelsson, B., Troein, C.: Phys. Rev. Lett. 90, 098701 (2003) CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Drossel, B. Mihaljev, T., Greil, F.: Phys. Rev. Lett. 94, 088701 (2005) CrossRefADSGoogle Scholar
  14. 14.
    Fontanari, J.F., Köberle, R.: J. Phys. 49, 13 (1988) Google Scholar
  15. 15.
    Bollé, D., Busquets Blanco, J.: Eur. Phys. J. B 47, 281 (2005) CrossRefADSGoogle Scholar
  16. 16.
    Potts, R.B.: Proc. Camb. Phil. Soc. 48, 106 (1952) MATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Bollé, D., Busquets Blanco, J.: Eur. Phys. J. B 42, 397 (2004) CrossRefADSGoogle Scholar
  18. 18.
    Nishimori, H.: TITECH report (1997) Google Scholar
  19. 19.
    Li, F., Long, T., Lu, Y., Ouyang, Q., Tang, C.: Proc. Nat. Acad. Sci. USA 101, 4781 (2004) CrossRefADSGoogle Scholar
  20. 20.
    Menyhárd, N., Ódor, G.: J. Phys. A Math. Gen. 28, 4505 (1995) MATHCrossRefADSGoogle Scholar
  21. 21.
    Ódor, G., Menyhárd, N.: Phys. Rev. E 73, 036130 (2006) CrossRefADSGoogle Scholar
  22. 22.
    Jensen, I.: Phys. Rev. E 50, 3623 (1994) CrossRefADSGoogle Scholar
  23. 23.
    Menyhárd, N., Ódor, G.: J. Phys. A Math. Gen. 29, 7739 (1996) MATHCrossRefADSGoogle Scholar
  24. 24.
    Glauber, R.J.: J. Math. Phys. 4, 294 (1963) MATHCrossRefMathSciNetADSGoogle Scholar
  25. 25.
    Cardy, J., Täuber, U.C.: Phys. Rev. Lett. 77, 4780 (1996) CrossRefADSGoogle Scholar
  26. 26.
    Privman, V.: Nonequilibrium Statistical Mechanics in One Dimension. Cambridge University Press, Cambridge (1997) MATHGoogle Scholar
  27. 27.
    Hinrichsen, H.: Adv. Phys. 49, 815 (2000) CrossRefADSGoogle Scholar
  28. 28.
    Ódor, G.: Rev. Mod. Phys. 76, 663 (2004) CrossRefADSGoogle Scholar
  29. 29.
    Jensen, I.: J. Phys. A Math. Gen. 26, 3921 (1993) CrossRefADSGoogle Scholar
  30. 30.
    ben-Avraham, D., Leyvraz, F., Redner, S.: Phys. Rev. E 50, 1843 (1990) CrossRefADSGoogle Scholar
  31. 31.
    Zhong, D., ben-Avraham, D.: Phys. Lett. A 209, 333 (1995) CrossRefADSGoogle Scholar
  32. 32.
    Janseen, H.K.: Phys. Rev. Lett. 78, 2890 (1997) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Filippo Radicchi
    • 1
  • Daniele Vilone
    • 1
  • Hildegard Meyer-Ortmanns
    • 1
  1. 1.School of Engineering and ScienceJacobs University BremenBremenGermany

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