Universality Under Conditions of Self-tuning
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- Peters, O. & Girvan, M. J Stat Phys (2010) 141: 53. doi:10.1007/s10955-010-0039-0
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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.