  The SED of blazars show significant curvature. In this paper, we study the
curvature properties for a large sample of Fermi/LAT bright blazars based on
quasi-simultaneous SED. Both SEDs of synchrotron and inverse Compton (IC)
components are fitted by a log-parabolic law in log_v-log_vfv diagram. The
second-degree term of log-parabola measures the curvature of SED. We find a
statistically significant correlation between synchrotron peak frequency and
its curvature. This result is in agreement with the theoretical prediction, and
confirms previous studies, which dealt with single source with various epoch
observations or a small sample. If a broken power-law is employed to fit the
SED, the difference between the two spectral indexes (alpha2-alpha1) can be
considered as a "surrogate" of the SED curvature. We collect spectral
parameters of a sample blazars from literature, and find a correlation between
the synchrotron peak frequency and the spectral difference. We do not find a
significant correlation between the IC peak frequency and its curvature, which
may be caused by complicated seed photon field. It is also found that the
synchrotron curvatures are on average larger than that of IC curvatures, and
there is no correlation between these two parameters. As suggested by previous
works in literature, both the log-parabolic law of SED and above correlation
can be explained by statistical and/or stochastic particle accelerations.
Stochastic particle acceleration predicts a different slope of the correlation
from that of statistical one, and our result seems favor stochastic
acceleration mechanisms and emission processes. Some of other evidences also
seem to support that the electron energy distribution (and/or synchrotron SED)
may be log-parabolic, which include SED modeling, particle acceleration
simulation, and comparisons between some predictions and empirical
relations/correlations.
