  By using frustration-preserving hard-spin mean-field theory, we investigated
the phase transition dynamics in the three-dimensional field-free $\pm J$ Ising
spin glass model. As the temperature $T$ is decreased from paramagnetic phase
at high temperatures, with a rate $\omega=-dT/dt$ in time $t$, the critical
temperature depends on the cooling rate through a clear power-law $\omega^a$.
With increasing antiferromagnetic bond fraction $p$, the exponent $a$ increases
for the transition into the ferromagnetic case for $p<p_\text{c}$, and
decreases for the transition into the spin glass phase for $p>p_\text{c}$,
signaling the ferromagnetic-spin glass phase transition at
$p_\text{c}\approx0.22$. The relaxation time is also investigated, at adiabatic
case $\omega=0$, and it is found that the dynamic exponent $z\nu$ increases
with increasing $p$.
