Journal of Statistical Physics

, Volume 141, Issue 1, pp 53–59 | Cite as

Universality Under Conditions of Self-tuning

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Abstract

We study systems with a continuous phase transition that tune their parameters to maximize a quantity that diverges solely at a unique critical point. Varying the size of these systems with dynamically adjusting parameters, the same finite-size scaling is observed as in systems where all relevant parameters are fixed at their critical values. This scheme is studied using a self-tuning variant of the Ising model. It is contrasted with a scheme where systems approach criticality through a target value for the order parameter that vanishes with increasing system size. In the former scheme, the universal exponents are observed in naïve finite-size scaling studies, whereas in the latter they are not.

Keywords

Universality Self-tuning 

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References

  1. 1.
    Alava, M.J., Laurson, L., Vespignani, A., Zapperi, S.: Comment on “Self-organized criticality and absorbing states: Lessons from the Ising model”. Phys. Rev. E 77, 048101 (2008) CrossRefADSGoogle Scholar
  2. 2.
    Andrews, T.: The Bakerian lecture: On the continuity of the gaseous and liquid states of matter. Philos. Trans. R. Soc. 159, 575–590 (1869) CrossRefGoogle Scholar
  3. 3.
    Cardy, J.: Scaling and Renormalization in Statistical Physics. Cambridge University Press, Cambridge (1996) Google Scholar
  4. 4.
    Christensen, K., Moloney, N., Peters, O., Pruessner, G.: Avalanche behavior in an absorbing state Oslo model. Phys. Rev. E 70, 067101 (2004) CrossRefADSGoogle Scholar
  5. 5.
    Dickman, R., Vespignani, A., Zapperi, S.: Self-organized criticality as an absorbing-state phase transition. Phys. Rev. E 57, 5095–5105 (1998) CrossRefADSGoogle Scholar
  6. 6.
    Dickman, R., Munoz, M., Vespignani, A., Zapperi, S.: Paths to self-organized criticality. Braz. J. Phys. 30, 27–41 (2000) Google Scholar
  7. 7.
    Dickman, R., Alava, M., Munoz, M., Peltola, J., Vespignani, A., Zapperi, S.: Critical behavior of a one-dimensional fixed-energy stochastic sandpile. Phys. Rev. E 64, 056104 (2001) CrossRefADSGoogle Scholar
  8. 8.
    Fraysse, N., Sornette, A., Sornette, D.: Critical phase-transitions made self-organized—proposed experiments. J. Phys. I 3, 1377–1386 (1993) CrossRefGoogle Scholar
  9. 9.
    Hsiao, P., Monceau, P., Perreau, M.: Magnetic critical behavior of fractals in dimensions between 2 and 3. Phys. Rev. B 62, 13856–13859 (2000) CrossRefADSGoogle Scholar
  10. 10.
    Lubeck, S.: Universal scaling behavior of non-equilibrium phase transitions. Int. J. Mod. Phy. B 18, 3977–4118 (2004) CrossRefADSGoogle Scholar
  11. 11.
    Manna, S.S.: 2-State model of self-organized criticality. J. Phys. A 24, L363–L369 (1991) CrossRefMathSciNetADSGoogle Scholar
  12. 12.
    Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in C: The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (2002) Google Scholar
  13. 13.
    Privman, V., Hohenberg, P.C., Aharony, A.: Universal critical-point amplitude relations. In: Domb, C., Liebowitz, J.L. (eds.) Phase Transitions and Critical Phenomena. Academic Press, San Diego (1991) Google Scholar
  14. 14.
    Pruessner, G., Peters, O.: Self-organized criticality and absorbing states: Lessons from the Ising model. Phys. Rev. E 73, 025106 (2006) CrossRefADSGoogle Scholar
  15. 15.
    Pruessner, G., Peters, O.: Reply to “Comment on ‘Self-organized criticality and absorbing states: Lessons from the Ising model”. Phys. Rev. E 77, 048102 (2008) CrossRefADSGoogle Scholar
  16. 16.
    Tank, C., Bak, P.: Mean field theory of self-organized critical phenomena. J. Stat. Phys. 51, 797–802 (1988) CrossRefADSGoogle Scholar
  17. 17.
    Williams, J.K.: Monte Carlo estimate of the dynamical critical exponent of the 2D kinetic Ising model. J. Phys. A 18, 49–60 (1985) CrossRefMathSciNetADSGoogle Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and Grantham Institute for Climate ChangeImperial College LondonLondonUK
  2. 2.Department of Physics and Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

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