Abstract
We show that the relaxation dynamics near a glass transition with continuous
ergodicity breaking can be endowed with a geometric interpretation based on
percolation theory. At mean-field level this approach is consistent with the
mode-coupling theory (MCT) of type-A liquid-glass transitions and allows to
disentangle the universal and nonuniversal contributions to MCT relaxation
exponents. Scaling predictions for the time correlation function are
successfully tested in the F12 schematic model and facilitated spin systems on
a Bethe lattice. Our approach immediately suggests the extension of MCT scaling
laws to finite spatial dimensions and yields new predictions for dynamic
relaxation exponents below an upper critical dimension of 6.
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