The three-dimensional $\pm J$ Heisenberg spin-glass model is investigated by the non-equilibrium relaxation method from the paramagnetic state. Finite-size effects in the non-equilibrium relaxation are analyzed, and the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility in the infinite-size system are obtained. The finite-time scaling analysis gives the spin-glass transition at $T_{ \rm sg}/J=0.21_{ -0.02}^{ +0.01}$ and the chiral-glass transition at $T_{ \rm cg}/J=0.22_{ -0.03}^{ +0.01}$. The results suggest that both transitions occur simultaneously. The critical exponent of the spin-glass susceptibility is estimated as $\gamma_{ \rm sg}= 1.7 \pm 0.3$, which makes an agreement with the experiments of the insulating and the canonical spin-glass materials.
Categories: cond-mat.dis-nn