Logarithmic relaxation in a kinetically constrained model

We present Monte Carlo simulations on a coarse-grained model for relaxation in binary mixtures. 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) is permitted according to kinetic constraints determined by the mobilities of neighboring cells. We introduce two types of cells ("fast" and "slow") with very different rates for spin flip. Fast cells display anomalous relaxation, characterized by a concave-to-convex crossover in dynamic 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 polymer blends.