Impact of tunable interactions on emergent behavior in a random field Ising model with feedback

Traditional condensed matter and statistical physics approaches coarse-grain over small-scale interactions to predict emergent behavior, but in biological systems small-scale interactions can be altered by emergent macroscopic properties via feedback. As a toy model for biological systems that can adjust small-scale tunable degrees of freedom based on larger scale emergent properties, we investigate an Ising model with a tunable random field at every site. These site-specific ‘fields’ experience a negative feedback driven by the emergent magnetization. A mean-field version of this model with zero disorder in the initial conditions was recently proposed to study neural activity, leading to oscillations and scale free avalanches that match observations from brain recordings1. As we are interested in mechanical biological networks in 2 or 3 dimensions and also where the disorder is prevalent, we perform numerical simulations of a 2D Random field Ising Model at zero temperature with this feedback and observe a critical point separating the paramagnetic and the ferromagnetic regimes. In the latter regime, system spanning avalanches drive oscillations with timescales that are modified by the disorder. Since there is a diverging length scale, we also study feedback where the magnetization is only averaged over a local, finite length scale.

1 Lombardi, F., Pepić, S., Shriki, O. et al. Nat Comput Sci 3, 254–263 (2023)