Non-self-averaging in Ising spin glasses; hyperuniversality

Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized inter-sample variance) parameter U22(T,L) for the spin glass susceptibility (and for higher moments Unn(T,L)) is reported for dimensions 2, 3, 4, 5 and 7. In each dimension d the non-self-averaging parameters in the paramagnetic regime vary with the sample size L and the correlation length ξ(T,L) as Unn(β, L) = [Kdξ(T,L)/L] , and so follow a renormalization group law due to Aharony and Harris [1]. Empirically, it is found that theKd values are independent of d to within the statistics. The maximum values [Unn(T, L)]max are almost independent of L in each dimension, and remarkably the estimated thermodynamic limit critical [Unn(T, L)]max peak values are also dimension-independent to within the statistics and so are ”hyperuniversal”. These results show that the form of the spin-spin correlation function distribution at criticality in the large L limit is independent of dimension within the ISG family. Inspection of published non-self-averaging data for 3D Heisenberg and XY spin glasses the light of the Ising spin glass non-self-averaging results show behavior incompatible with a spin-driven ordering scenario, but compatible with that expected on a chiral-driven ordering interpretation.