Scaling laws and relaxation rate at desynchronization in coupled oscillators

TL;DR

This paper investigates phase transitions in a non-locally coupled oscillator model, revealing critical behavior at a first order transition with diverging relaxation times and specific scaling laws.

Contribution

It demonstrates that non-local interactions can induce critical phenomena at first order phase transitions, supported by numerical and analytical analysis of scaling laws.

Findings

Order parameter scaling exponent is 1/2.

Relaxation time diverges near the transition.

Finite size scaling and data collapse verify homogeneity.

Abstract

Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order transition i.e an abrupt jump in order parameter, we obtain the order parameter scaling exponent $1/2$ and show that the relaxation time diverges near the transition point, both numerically and analytically. We also verify a finite time finite size scaling by considering a correlation measure in the discrete set of all interacting units. Due to divergence in correlation measure at the transition point, the order parameter becomes a homogeneous function of all the relevent parameters. The homogeneity assumption is numerically verified using data collapse method. Various finite size scaling relations and exponents are also obtained. This study suggests that presence of non local interactions may allow for critical behaviour at a first order transition.