  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 $U_{22}(T,L)$ for the spin glass
susceptibility (and for higher moments $U_{nn}(T,L)$) 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 $\xi(T,L)$ as $U_{nn}(\beta,L) = [K_{d}\xi(T,L)/L]^d$, and
so follow a renormalization group law due to Aharony and Harris (1991).
Empirically, it is found that the $K_{d}$ values are independent of d to within
the statistics. The maximum values $[U_{nn}(T,L)]_{\max}$ are almost
independent of L in each dimension, and remarkably the estimated thermodynamic
limit critical $[U_{nn}(T,L)]_{\max}$ 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.
