Fig. 5: Spin model.

a Population activity as a function of \(\beta =1/T\), relative to the critical point \({\beta }_{c}=1/{T}_{c}\). For \(T > {T}_{c}\), the system is disordered and the average population activity is zero. For \(T < {T}_{c}\), the system is ordered and a spontaneous population activity emerges and settles in either a negative or a positive value (depending on the initial conditions). b At the critical point (blue), the correlation function is a power law, with a power exponent \(\widetilde{\eta }\) close to the one measured in the fMRI data. The correlation function is shown for three example temperatures, also shown in (a) (red: supercritical; blue: critical; purple: subcritical). c Exponent \(\widetilde{\eta }\) as a function of \(\beta /{\beta }_{c}\). d Variance \(V\) of coarse-grained variables as a function of cluster size \(K\), for the three example temperatures. e Exponent \(\widetilde{\alpha }\) as a function of \(\beta /{\beta }_{c}\). f Eigenvalues of the covariance matrix as a function of their relative rank, at the critical point, for clusters of different sizes. g Exponent \(\mu\) as a function of \(\beta /{\beta }_{c}\). In (a), (b), (d) and (f), the connectivity used was the EDR. In (c), (e), and (g): filled symbols indicate explained variance ratios favoring the power law model over the exponential model, i.e., \({R}_{{EV}} > 1\) (see also Supplementary Fig. S5); exponent estimation errors are smaller than the symbols; the horizontal line indicates the empirically measured exponent.