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

TL;DR

This study uses large-scale Monte Carlo simulations to investigate the spin-chirality decoupling in the 3D Heisenberg spin glass, providing numerical evidence that the chiral-glass order occurs at a higher temperature than the spin-glass order.

Contribution

The paper presents the first stable and accurate estimates of the transition temperatures and critical exponents for both chiral-glass and spin-glass phases in the 3D Heisenberg spin glass.

Findings

Chiral-glass transition temperature T_CG = 0.142 ± 0.001

Spin-glass transition temperature T_SG = 0.131^{+0.001}_{-0.006}

Evidence supports spin-chirality decoupling in the model

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 $T_{{\rm CG}}$ and $T_{{\rm SG}}$ by the $L\rightarrow \infty$ 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, $T_{{\rm CG}}=0.142\pm 0.001$ and $T_{{\rm SG}}=0.131^{+0.001}_{-0.006}$. 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, $\nu_{{\rm CG}}=1.36\pm 0.10$ and $\eta_{{\rm CG}}=0.49\pm 0.10$, consistently with the corresponding experimental exponents of canonical SG. Implications to the chirality scenario of experimental SG ordering is discussed.