Spin-Glass and Chiral-Glass Transitions in a $\pm J$ Heisenberg Spin-Glass Model in Three Dimensions

Abstract

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 $T_{\mathrm{sg}}/J=0.21_{-0.02}^{+0.01}$ and the chiral-glass transition at $T_{\mathrm{cg}}/J=0.22_{-0.03}^{+0.01}$. The results suggest that both transitions occur simultaneously. The critical exponent of the spin-glass susceptibility is estimated as ${\gamma }_{\mathrm{sg}}=1.7\pm 0.3$, which makes an agreement with the experiments of the insulating and the canonical spin-glass materials.

4 pages, 2 figures

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