Monte Carlo studies of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass

Abstract

An extensive equilibrium Monte Carlo simulation is performed on the 3D isotropic Heisenberg SG model with the random nearest-neighbor Gaussian coupling, with particular interest in its chiral-glass (CG) and spin-glass (SG) orderings. For this model, the possibility of the spin-chirality decoupling, {\it 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 (BC). In locating the CG and SG transition temperatures $T_{\mathrm{CG}}$ and $T_{\mathrm{SG}}$ by the $L\to \infty$ extrapolation, a variety of independent physical quantities under the both BC are computed and utilized to get larger number of degrees of freedom (NDF). Thanks to the large NDF up to 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 by use of 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 ${\eta }_{\mathrm{CG}}=0.49\pm 0.10$, consistently with the corresponding experimental exponents of canonical SG. Implications to the chirality scenario of experimental SG ordering is discussed.

Paragraphs and equations are added to the last subsection of Section V. To appear in Phys. Rev. B

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