Phase transition dynamics in the three-dimensional ±J Ising model

By using frustration-preserving hard-spin mean-field theory, we investigated the phase-transition dynamics in the three-dimensional field-free +/- 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(c) and decreases for the transition into the spin-glass phase for p > p(c), signaling the ferromagnetic - spin-glass phase transition at p(c) approximate to 0.22. The relaxation time is also investigated in the adiabatic case omega = 0 and the dynamic exponent zv is found to increase with increasing p.