Is there existing research suggesting that critical systems' power spectra are correlated with their eigenspectra?

Question

I am interested in how the spatial and temporal spectral exponents – in other words the exponents of the power spectrum and eigenspectrum – of a high dimensional system at criticality are related. It is known that the dynamics of complex systems operating at criticality (I am working with neural data but this may also apply to lattice models like the Ising model where the aforementioned spectra are power law like) exhibit strong correlation throughout space and time. I am having trouble finding literature on whether and how these two spectra and their exponents are correlated with one another, and looking for any pointers on existing research and/or mathematical explanations behind this.