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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 $U_{22}(T,L)$ 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 $ξ(T,L)$ as $U_{nn}(β,L) = [K_{d}ξ(T,L)/L]^d$, 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.