Stretched exponential relaxation on the hypercube and the glass transition

We study random walks on the dilute hypercube using an exact enumeration Master equation technique, which is much more efficient than Monte Carlo methods for this problem. For each dilution p the form of tho relaxation of the memory function q(t) can be accurately parametrized by a stretched exponential q(t) = exp(-(t/tau)(beta)) over several orders of magnitude in q(t). As the critical dilution for percolation p(c) is approached, the time constant tau (p) tends to diverge and the stretching exponent beta (p) drops towards 1/3. As the same pat tern of relaxation is observed in a wide class of glass formers, the fractal like morphology of the giant cluster in the dilute hypercube appears to be a good representation of the coarse grained phase space in these systems. For these glass formers the glass transition mag be pictured as a percolation transition in phase space.