Mean-Field and Anomalous Behavior on a Small-World Network

M. B. Hastings

Published 2003-04-23, updated 2003-05-01Version 2

We use scaling results to identify the crossover to mean-field behavior of equilibrium statistical mechanics models on a variant of the small world network. The results are generalizable to a wide-range of equilibrium systems. Anomalous scaling is found in the width of the mean-field region, as well as in the mean-field amplitudes. Finally, we consider non-equilibrium processes.