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Interface Motion and Pinning in Small World Networks

Denis Boyer·Octavio Miramontes
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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.

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Denis Boyer, Octavio Miramontes. 2003-01-30. Interface Motion and Pinning in Small World Networks. https://doi.org/10.1103/physreve.67.035102

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