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We consider a mean-field model of coupled phase oscillators with quencheddisorder in the natural frequencies and coupling strengths. A fraction $p$ ofoscillators are positively coupled, attracting all others, while the remainingfraction $1-p$ are negatively coupled, repelling all others. The frequenciesand couplings are deterministically chosen in a manner which correlates them,thereby correlating the two types of disorder in the model. We first explorethe effect of this correlation on the system's phase coherence. We find thatthere is a a critical width $\gamma_c$ in the frequency distribution belowwhich the system spontaneously synchronizes. Moreover, this $\gamma_c$ isindependent of $p$. Hence, our model and the traditional Kuramoto model(recovered when $p=1$) have the same critical width $\gamma_c$. We next explorethe critical behavior of the system by examining the finite-size scaling andthe dynamic fluctuation of the traditional order parameter. We find that themodel belongs to the same universality class as the Kuramoto model withdeterministically (not randomly) chosen natural frequencies for the case of$p<1$.

Correlated disorder in the Kuramoto model: Effects on phase coherence, finite-size scaling, and dynamic fluctuations