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 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 $L\ensuremath{\rightarrow}\ensuremath{\infty}$ 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, ${T}_{\mathrm{CG}}=0.142\ifmmode\pm\else\textpm\fi{}0.001$ and ${T}_{\mathrm{SG}}=0.{131}_{\ensuremath{-}0.006}^{+0.001}$. 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, ${\ensuremath{\nu}}_{\mathrm{CG}}=1.36\ifmmode\pm\else\textpm\fi{}0.10$ and ${\ensuremath{\eta}}_{\mathrm{CG}}=0.49\ifmmode\pm\else\textpm\fi{}0.10$, consistent with the corresponding experimental exponents of canonical SG. Implications for the chirality scenario of experimental SG ordering are discussed.