Timescales in the thermal dynamics of magnetic dipolar clusters

The collective behavior of thermally active structures offers clues on the emergent degrees of freedom and the physical mechanisms that determine the low-energy state of a variety of systems. Here, the thermally active dynamics of magnetic dipoles at square plaquettes is modeled in terms of Brownian oscillators in contact with a heat bath. Solution of the Langevin equation for a set of interacting x-y dipoles allows the identification of the timescales and correlation length that reveal how interactions, temperature, damping, and inertia may determine the frequency modes of edge and bulk magnetic mesospins in artificial dipolar systems.