Non-self-averaging in Ising spin glasses and hyperuniversality

P. H. Lundow , Ian Campbell (1)

1 L2C - Laboratoire Charles Coulomb

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 $U_{nn}(β,L)=[K_dξ(T,L)/L]^d$ and so follow a renormalization group law due to Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. 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.

Domaines: Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

P. H. Lundow, Ian Campbell. Non-self-averaging in Ising spin glasses and hyperuniversality. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2016, 93 (1), pp.012118. ⟨10.1103/PhysRevE.93.012118⟩. ⟨hal-01289903⟩