Universality Under Conditions of Self-tuning
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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.
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- 3.Cardy, J.: Scaling and Renormalization in Statistical Physics. Cambridge University Press, Cambridge (1996) Google Scholar
- 6.Dickman, R., Munoz, M., Vespignani, A., Zapperi, S.: Paths to self-organized criticality. Braz. J. Phys. 30, 27–41 (2000) Google Scholar
- 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.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