An extensive equilibrium Monte Carlo simulation is performed on the three-dimensional isotropic Heisenberg spin-glass (SG) model with the random nearest-neighbor Gaussian coupling, with particular interest in its chiral-glass (CG) and SG orderings. For this model, the possibility of the spin-chirality decoupling, i.e., the CG order setting in at a higher temperature than that of the SG order, was suggested earlier but still remains controversial. We simulate the model up to the maximum size (linear dimension) $L=48$ under both periodic and open boundary conditions (BCs). In locating the CG and SG transition temperatures $T_{\mathrm{CG}}$ and $T_{\mathrm{SG}}$ with the $L\to \infty$ extrapolation, a variety of independent physical quantities under both BCs are computed and utilized to get larger number of degrees of freedom (NDF). Because of the large NDF up to $\text{NDF}=43$, we succeed in obtaining stable and accurate estimates of the CG and SG transition temperatures, $T_{\mathrm{CG}}=0.142\pm 0.001$ and $T_{\mathrm{SG}}=0.{131}_{-0.006}^{+0.001}$. No sign of the size crossover is observed. For larger $L$, the CG correlation length progressively outgrows the SG correlation length at low temperatures. These results provide strong numerical support for the spin-chirality decoupling. The critical exponents associated with the CG and SG transitions are evaluated using the finite-size scaling with the scaling correction. For the CG transition, we get the CG exponents, ${\nu }_{\mathrm{CG}}=1.36\pm 0.10$ and ${\eta }_{\mathrm{CG}}=0.49\pm 0.10$, consistent with the corresponding experimental exponents of canonical SG. Implications for the chirality scenario of experimental SG ordering are discussed.

• Received 4 December 2019
• Revised 9 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.014434