Nonequilibrium relaxation analysis of the spin-glass correlation length

Relaxation functions of the spin-glass correlation length are investigated in the three-dimensional ±J XY model. The algebraic divergence is observed at the spin-glass transition temperature, T_sg ≃ 0.45. The finite-time scaling analysis provides results consistent with our previous scaling analysis of the spin-glass susceptibility. The relaxation functions in the low-temperature phase exhibit the same behavior with the Ising spin glass: the exponent is linearly dependent on the temperature as 1/z(T) ≃ 0.21T/T_sg. Relaxation functions of the chiral-glass correlation length do not exhibit such behavior as the spin-glass ones do. All the findings suggest that the transition is driven by the spin degrees of freedom.