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

TL;DR

This paper investigates how equilibrium statistical mechanics models on small-world networks transition to mean-field behavior, revealing anomalous scaling and extending analysis to non-equilibrium processes.

Contribution

It identifies the crossover to mean-field behavior on small-world networks and uncovers anomalous scaling in both equilibrium and non-equilibrium systems.

Findings

Crossover to mean-field behavior on small-world networks

Anomalous scaling in mean-field region width and amplitudes

Extension of results to non-equilibrium processes

Abstract

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.