Anomalous Size Dependence of Relaxational Processes

Abstract

We consider relaxation processes that exhibit a stretched exponential behavior. We find that in those systems, where the relaxation arises from two competing exponential processes, the size of the system may play a dominant role. Above a crossover time ${t}_{\ifmmode\times\else\texttimes\fi{}}$ that depends logarithmically on the size of the system, the relaxation changes from a stretched exponential to a simple exponential decay, where the decay rate also depends logarithmically on the size of the system. This result is relevant to large-scale Monte Carlo simulations and should be amenable to experimental verification in low-dimensional and mesoscopic systems.