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