Interface motion and pinning in small-world networks

We show that the nonequilibrium dynamics of systems with many interacting elements located on a small-world network can be much slower than on regular networks. As an example, we study the phase ordering dynamics of the Ising model on a Watts-Strogatz network, after a quench in the ferromagnetic phase at zero temperature. In one and two dimensions, small-world features produce dynamically frozen configurations, disordered at large length scales, analogous to random field models. This picture differs from the common knowledge (supported by equilibrium results) that ferromagnetic shortcut connections favor order and uniformity. We briefly discuss some implications of these results regarding the dynamics of social changes.