Fig. 1

a–d Phase diagrams for the empirical data. e–h Phase diagrams for the SK model. a, e: ∣m∣. b, f: q. c, g: χ_SG. d, h: χ_uni. In a, d the crosses represent the mean and standard deviation of the J_ij estimated for the entire population of the participants, i.e., (\(\hat{\mu }\), \(\hat{\sigma }\)). In c a circle represents a participant. In a and e we plot ∣m∣ instead of m. This is because averaging over simulations and over realizations of J would lead to m ≈ 0 due to symmetry breaking, even if m ≠ 0 in theory such as in the ferromagnetic phase. i χ_SG as a function of σ, with \(\mu =\hat{\mu }\) being fixed. j χ_uni as a function of μ, with \(\sigma =\hat{\sigma }\) being fixed. In i and j, the curves are the cross-sectional view of c and d, respectively, along the dashed line in c or d. The circles in i and j represent the individual participants and are the projection of the circles in c and d onto the dashed line. k Scaling behavior of χ_SG when the system size \({N}^{\prime}\) is varied. The value of σ = σ_peak that maximizes χ_SG is plotted against \(1/{N}^{\prime}\) in the inset. The dashed line is the linear regression based on the six data points, \({N}^{\prime}=40,60,80,120,160\), and 264. The coefficient of determination is denoted by R².