Fig. 4: Studying the spectra of odd operators at the critical point.
From: The quantum transition of the two-dimensional Ising spin glass
a, The decay of the sample-averaged correlation function C(τ) (equation (14)) approaches a power law as L increases. The dashed line is a guide for the eyes. Indeed, we needed to represent C(τ) in terms of \(\widetilde{\tau }=({L}_{\tau }/{\rm{\pi }})\sin ({\rm{\pi }}\tau /{L}_{\tau })\) to avoid distortions due to the PBCs (\(\widetilde{\tau }\) and τ are almost identical for small τ/Lτ). b, Empirical distribution function F(η) as a function of \(\log \eta \) for all our system sizes. Note that we can compute only up to some L-dependent F because our largest Lτ is not large enough to allow for a safe determination of η in some samples. c, For large η, the asymptotic behaviour \(F(\eta )=1-B/{\eta }^{b}\) is evinced by the linear behaviour (in logarithmic scale) of 1 − F as a function of η. We fond b ≈ 0.8. The dashed line is a guide for the eyes. Points in a, b, and c are statistical averages, and errors are one standard deviation. Our data set is fully described in Extended Data Table 1.
