  We investigate a critical exponent related to synchronization transition in
globally coupled nonidentical phase oscillators. The critical exponents of
susceptibility, correlation time, and correlation size are significant
quantities to characterize fluctuations in coupled oscillator systems of large
but finite size and understand a universal property of synchronization. These
exponents have been identified for the sinusoidal coupling but not fully
studied for other coupling schemes. Herein, for a general coupling function
including a negative second harmonic term in addition to the sinusoidal term,
we numerically estimate the critical exponent of the correlation size, denoted
by $\nu_+$, in a synchronized regime of the system by employing a
non-conventional statistical quantity. First, we confirm that the estimated
value of $\nu_+$ is approximately 5/2 for the sinusoidal coupling case, which
is consistent with the well-known theoretical result. Second, we show that the
value of $\nu_+$ increases with an increase in the strength of the second
harmonic term. Our result implies that the critical exponent characterizing
synchronization transition largely depends on the coupling function.
