Universality under conditions of self-tuning

TL;DR

This paper investigates systems that self-tune their parameters to reach a critical point, demonstrating that such self-tuning leads to universal finite-size scaling behavior similar to fixed-parameter systems.

Contribution

It introduces a self-tuning variant of the Ising model and compares its scaling behavior to traditional approaches, highlighting the emergence of universality under self-tuning conditions.

Findings

Self-tuning systems exhibit universal finite-size scaling.

Traditional schemes may not show universal exponents.

Self-tuning can recover critical scaling in finite systems.

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 naive finite-size scaling studies, whereas in the latter they are not.