Abstract
Many complex systems exhibit large fluctuations both across space and over time. These fluctuations have often been linked to the presence of some kind of critical phenomena, where it is well known that the emerging correlation functions in space and time are closely related to each other. Here we test whether the time correlation properties allow systems exhibiting a phase transition to self-tune to their critical point. We describe results in three models: the 2D Ising ferromagnetic model, the 3D Vicsek flocking model and a small-world neuronal network model. We demonstrate that feedback from the autocorrelation function of the order parameter fluctuations shifts the system towards its critical point. Our results rely on universal properties of critical systems and are expected to be relevant to a variety of other settings.
Highlights
The system undergoes a second order phase transition at a critical temperature Tc , reflected in a steep change in magnetization as well as a sharp peak in susceptibility (Fig. 1A)
We show that a system can be tuned to the vicinity of its finite-size “critical” point using the first autocorrelation coefficient AC(1) of the order parameter fluctuations (we define AC(1) as in time-series analysis as the time correlation of the order parameter at t = 1 )
Because AC(1) peaks at the same point as the susceptibility, yet does so more smoothly than the susceptibility, a control feedback seems straightforward. This behavior of AC(1) near criticality responds to the notion of critical slowing down in both equilibrium and non-equilibrium critical dynamics by which perturbations take longer to dissipate near criticality
Summary
The system undergoes a second order phase transition at a critical temperature Tc , reflected in a steep change in magnetization as well as a sharp peak in susceptibility (Fig. 1A). To demonstrate control we proceed by choosing an initial random temperature and simulate the dynamics for some large number of Montecarlo (MC) steps, which we denote as an “adaptation iteration step” indexed by i. We note that the successive values of the parameters (order, control and AC(1)) obtained during the adaptive simulations over-imposes well (i.e., matches) those obtained from equilibrium simulations.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
