  We have studied the dynamic and static critical behavior of spin glass
transition in insulating La$_{0.9}$Sr$_{0.1}$CoO$_3$ single crystal by ac
susceptibility and dc magnetization measurements in the vicinity of its
freezing temperature ($T_f$). The dynamic scaling analysis of the frequency
dependence of ac susceptibility data yields the characteristic time constant
$\tau_{0}$=1.6(9)$\times10^{-12}$ s, the dynamic critical exponent
$z\nu$=9.5(2), and a frequency dependence factor
$K$=$\Delta$$T_{f}/T_{f}$($\Delta$$log$$f$)=0.017, indicating that the sample
enters into a canonical spin-glass phase below $T_{f}$=34.8(2) K. The scaling
analysis of non-linear magnetization in the vicinity of $T_{f}$ through the
static scaling hypothesis yields critical exponents $\beta$=0.89(1) and
$\gamma$=2.9(1), which match well with that observed for well known
three-dimensional (3D) Heisenberg spin glasses. From the longitudinal component
of zero-field-cooled and field-cooled magnetization measurement we have
constructed the $H-T$ phase diagram which represents the field evolution of two
characteristic temperatures: the upper one, $T_{w}(H)$, indicates the onset of
spin freezing in a uniform external field $H$, while the lower one, $T_{s}(H)$,
marks the onset of strong irreversibility of the frozen state. The low field
$T_{s}(H)$ follows the critical line suggested by d'Almeida-Thouless model for
canonical spin glass, whereas the $T_{w}(H)$ exhibits a reentrant behavior with
a maximum in the $T_{w}(H)$ at a nonzero field above which it follows the
Gabay-Toulouse (GT) critical line which is a characteristic of Heisenberg spin
glass. The re-entrant behavior of the GT line resembles that predicted
theoretically for $n$-component vector spin glasses in the presence of a
uniaxial anisotropy field.
