Non-self-averaging in Ising spin glasses and hyperuniversality.

Abstract

Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized intersample 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 [Phys. Rev. Lett. 77, 3700 (1996)PRLTAO0031-900710.1103/PhysRevLett.77.3700]. 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 practically 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 three-dimensional Heisenberg and XY spin glasses the light of the Ising spin glass non-self-averaging results show behavior which appears to be compatible with that expected on a chiral-driven ordering interpretation but incompatible with a spin-driven ordering scenario.