compare, we also plot twice the response of a single, isolated atom (green dashed line). b) Pictorial representation of the RG scheme. At each step of the RG flow the nearby pairs (identified by dashed circles) that mostly strongly interact via their near fields are identified, and replaced with atoms with different resonance frequencies (indicated by different colors) in such a way to produce an equivalent optical response. At the end of the RG process (last panel) the overall system is equivalent to an inhomogeneously broadened ensemble of weakly interacting atoms. c) Comparison between the maximum real refractive index predicted by the full coupled dipole simulations of identical atoms (blue points), and the equivalent, inhomogeneously broadened ensemble predicted by RG (green). For each value of density, the maximum index is obtained by optimizing over detuning. For comparison, the MB and LL models both predict a maximum index given by the orange curve. The inset compares the rescaled spectra ${
\text{Re}\;n
}(\Delta/\eta)$ of the RG (green) and full coupled dipole (blue) simulations, given the points at densities $\eta \gtrsim 2$. d) Rescaled probability distribution of effective, inhomogeneously broadened resonance frequencies $P(\omega_{\text{eff}}/\eta)$ obtained from the application of the RG scheme. Given 9 