Rhythmic behavior in a two-population mean field Ising model

TL;DR

This paper investigates how a two-population mean field Ising model can exhibit collective rhythmic behavior, transitioning from disorder to synchronized oscillations due to interaction strength differences.

Contribution

It introduces a two-population generalization of the mean field Ising model demonstrating how simple interaction mechanisms can generate macroscopic periodic rhythms.

Findings

System transitions from disordered to rhythmic phase

Different intra- and inter-population interactions induce oscillations

Robust periodic behavior emerges in specific parameter regions

Abstract

Many real systems comprised of a large number of interacting components, as for instance neural networks , may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean field Ising model with the scope of investigating simple mechanisms capable to generate rhythm in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intra-population interactions of different strengths suffices for the emergence of a robust periodic behavior.