Journal of Statistical Physics

, Volume 141, Issue 1, pp 53–59

Universality Under Conditions of Self-tuning


DOI: 10.1007/s10955-010-0039-0

Cite this article as:
Peters, O. & Girvan, M. J Stat Phys (2010) 141: 53. doi:10.1007/s10955-010-0039-0


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.


Universality Self-tuning 

Copyright information

© 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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