First-order like phase transition induced by quenched coupling disorder

We investigate the collective dynamics of a population of globally coupled XY model-type oscillators interacting with non-separable coupling interactions that are randomly chosen between two values, one positive the other negative. Oscillators are subject to thermal noise controlled by temperature T . For a finite ratio of positive versus negative coupling, we find that the system at T = 0 exhibits a first-order like phase transition from the incoherent state to the fully coherent state. We determine the critical threshold for this synchronization transition by performing a linear stability analysis of the fully coherent state. Our theoretical results are further supported by numerical simulations. The synchronization threshold induced by the type of random coupling considered here is identical to the one found in studies which consider uniform input or output strengths for each oscillator node [Hong and Strogatz, Phys. Rev. E 84, 046202 (2011); H. Hong and S. H. Strogatz, Phys. Rev. Lett. 106, 054102 (2011)]. Vice versa, when thermal noise is present (T > 0), the phase transition from the incoherent state to the partially ordered one is continuous and the system exhibits a higher value for the critical threshold.