Spin-chirality decoupling in the 3D Heisenberg spin glass
In plain words
In spin glasses whose atomic magnets can point in any direction, a second quantity, the chirality (the handedness of how neighboring spins twist), can also freeze. The question is whether spins and chiralities freeze at the same temperature or chiralities freeze first.
Precise statement
For the 3D isotropic Heisenberg spin glass with nearest-neighbor Gaussian couplings, determine whether the chiral-glass transition temperature $T_{\mathrm{CG}}$ equals the spin-glass transition temperature $T_{\mathrm{SG}}$ in the thermodynamic limit; if $T_{\mathrm{CG}} > T_{\mathrm{SG}}$, give the ratio and the universality class of each transition. Answer: yes or no, with $T_{\mathrm{CG}}/T_{\mathrm{SG}}$.
What would settle it
Equilibrium Monte Carlo on lattices large enough that finite-size crossings of spin and chiral correlation lengths converge to distinct or equal temperatures beyond statistical error.
Status in the literature
Simulations by the Kawamura group report $T_{\mathrm{CG}}$ slightly above $T_{\mathrm{SG}}$ (arXiv:1912.02502, 2019); other groups find a single transition within errors.