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By using frustration-preserving hard-spin mean-field theory, we investigatedthe phase transition dynamics in the three-dimensional field-free $\pm J$ Isingspin glass model. As the temperature $T$ is decreased from paramagnetic phaseat high temperatures, with a rate $\omega=-dT/dt$ in time $t$, the criticaltemperature depends on the cooling rate through a clear power-law $\omega^a$.With increasing antiferromagnetic bond fraction $p$, the exponent $a$ increasesfor the transition into the ferromagnetic case for $p<p_\text{c}$, anddecreases 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 adiabaticcase $\omega=0$, and it is found that the dynamic exponent $z\nu$ increaseswith increasing $p$.

Phase transition dynamics in the three-dimensional field-free $\pm J$ Ising model