ANOMALOUS SIZE DEPENDENCE OF RELAXATIONAL PROCESSES

We consider relaxation processes that exhibit a stretched exponential behavior. We find that in those systems, where the relaxation arises f rom two competing exponential processes, the size of the system may pl ay a dominant role. Above a crossover time t(x) that depends logarithm ically on the size of the system, the relaxation changes from a stretc hed exponential to a simple exponential decay, where the decay rate al so depends logarithmically on the size of the system. This result is r elevant to large-scale Monte Carlo simulations and should be amenable to experimental verification in low-dimensional and mesoscopic systems .