Mean-field and anomalous behavior on a small-world network.
We consider various equilibrium statistical mechanics models with combined short- and long-range interactions and identify the crossover to mean-field behavior, finding anomalous scaling in the width of the mean-field region, as well as in the mean-field amplitudes. We then show that this model enables us, in many cases, to determine the universal critical properties of systems on a small-world network. Finally, we consider nonequilibrium processes.
Hastings
M B
MB
Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. hastings@cnls.lanl.gov