Supplemental Material for Comment on "Excitons in Molecular Aggregates   with Levy Disorder: Anomalous Localization and Exchange Broadening of Optical   Spectra", Phys.Rev.Lett. 109, 259701 (https://arxiv.org/abs/1208.2779)
  In their Letter "Excitons in Molecular Aggregates with Levy Disorder: Anomalous Localization and Exchange Broadening of Optical Spectra", Eisfeld et al. predicted the existence of exchange broadening and blue-shift of the absorption band and a non-universal disorder scaling of the localisation length of absorption band excitons in J-aggregates with heavy-tailed disorder, which they contrasted with the previously analysed Gaussian and Lorentzian case. The observations were explained by another localisation mechanism, the chain segmentation by outliers in heavy tails of the disorder distribution. We argue that the previously known theory does not break down and consequently anticipates the properties of the absorption band investigated in the commented work. 
Agnieszka Werpachowska
cond-mat.dis-nn