Interface Motion and Pinning in Small World Networks

TL;DR

This paper investigates how small-world network structures influence the slow dynamics and formation of disordered states in the Ising model, contrasting with expectations from equilibrium behavior and highlighting implications for social dynamics.

Contribution

It demonstrates that small-world features can cause slow, frozen dynamics and disordered configurations in the Ising model, challenging the assumption that shortcuts promote order.

Findings

Small-world networks induce slow, frozen configurations in the Ising model.

Disordered states at large scales resemble random field models.

Contrasts with equilibrium results showing shortcuts favor order.

Abstract

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 of random field models. This picture differs from the common knowledge (supported by equilibrium results) that ferromagnetic short-cuts connections favor order and uniformity. We briefly discuss some implications of these results regarding the dynamics of social changes.