  We present Monte Carlo simulations in a modification of the
north-or-east-or-front model recently investigated by Berthier and Garrahan [J.
Phys. Chem. B 109, 3578 (2005)]. In this coarse-grained model for relaxation in
supercooled liquids, the liquid structure is substituted by a three-dimensional
array of cells. A spin variable is assigned to each cell, with values 0 or 1
denoting respectively unexcited and excited local states in a mobility field.
Change in local mobility (spin flip) for a given cell is permitted according to
kinetic constraints determined by the mobilities of neighboring cells. In this
work we keep the same kinetic constraints of the original model, but we
introduce two types of cells (denoted as "fast'' and "slow'') with very
different rates for spin flip. As a consequence, fast and slow cells exhibit
very different relaxation times for spin correlators. While slow cells exhibit
standard relaxation, fast cells display anomalous relaxation, characterized by
a concave-to-convex crossover in spin correlators by changing temperature or
composition. At intermediate state points logarithmic relaxation is observed
over three time decades. These results display striking analogies with dynamic
correlators reported in recent simulations on a bead-spring model for polymer
blends.
