Universality Under Conditions of Self-tuning |
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Authors: | Ole Peters and Michelle Girvan |
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Institution: | 1.Department of Mathematics and Grantham Institute for Climate Change,Imperial College London,London,UK;2.Department of Physics and Institute for Physical Science and Technology,University of Maryland,College Park,USA |
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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. |
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