Order-by-disorder in classical oscillator systems

TL;DR

This paper studies how noise can induce increased order in classical oscillator systems on hexagonal lattices with repulsive coupling, revealing a repeated order-by-disorder phenomenon similar to spin systems.

Contribution

It demonstrates the occurrence of multiple non-monotonic order-by-disorder effects in classical oscillator lattices under Gaussian noise, a novel insight into noise-induced synchronization.

Findings

Non-monotonic dependence of order on noise intensity

Multiple intervals of increased synchronization with noise

Noise-driven phase migration in a rough potential landscape

Abstract

We consider classical nonlinear oscillators on hexagonal lattices. When the coupling between the elements is repulsive, we observe coexisting states, each one with its own basin of attraction. These states differ by their degree of synchronization and by patterns of phase-locked motion. When disorder is introduced into the system by additive or multiplicative Gaussian noise, we observe a non-monotonic dependence of the degree of order in the system as a function of the noise intensity: intervals of noise intensity with low synchronization between the oscillators alternate with intervals where more oscillators are synchronized. In the latter case, noise induces a higher degree of order in the sense of a larger number of nearly coinciding phases. This order-by-disorder effect is reminiscent to the analogous phenomenon known from spin systems. Surprisingly, this non-monotonic evolution of the degree of order is found not only for a single interval of intermediate noise strength, but repeatedly as a function of increasing noise intensity. We observe noise-driven migration of oscillator phases in a rough potential landscape.