Patrick Charbonneau, Giorgio Parisi, Francesco Zamponi
Using numerical simulations we investigate the dimension evolution of the Stokes-Einstein relation violation in a simple glass forming system. The results strongly support the existence of an upper critical dimension d_u=8 above which the Stokes-Einstein relation is not violated, as predicted by the mean-field theory of glasses. In addition, the associated critical exponents evolve linearly in 8-d below d=8, which suggests that a suitable renormalization group expansion around the mean-field theory could provide a quantitative description of the glass problem. An analysis of single-particle motions in terms of Levy flights offers a possible scenario for relating these corrections to the mean-field description with the dynamical heterogeneity of glass formers.
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http://arxiv.org/abs/1210.6073
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