Comment on "Is there a breakdown of the Stokes-Einstein relation in Kinetically Constrained Models at low temperature?" by O. Blondel and C. Toninelli, arXiv:1307.1651

We consider the diffusion constant, D, of a probe particle coupled to the East model, extending previous numerical results for this model to encompass a total of twelve orders of magnitude in relaxation time, τ. Our considerations thus cover the full range of relaxation times relevant to experimental studies of reversible glass formers. Throughout this range, we show that the results of the model are consistent with a fractional Stokes-Einstein law, D \propto τ^{-ξ} with ξ \approx 0.77. The same data can also be fit by relating Dτ to the East model excitation concentration q, specifically, Dτ \sim 1/q^α with α \approx 1.6. In either case, breakdown of the Stokes-Einstein relation in this kinetically constrained model is unquestionable and large.

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