Comparison of voter and Glauber ordering dynamics on networks

TL;DR

This paper compares voter and Glauber dynamics on networks, revealing that Glauber dynamics can get trapped in metastable states while voter dynamics always reaches full order, with convergence time increasing with network size.

Contribution

It provides a numerical comparison of two simple ordering models on various network topologies, highlighting differences in their convergence and trapping behaviors.

Findings

Glauber dynamics often gets trapped in metastable states as network size increases.

Voter dynamics always converges to full order on finite networks.

Ordering time diverges with system size for both models.

Abstract

We study numerically the ordering process of two very simple dynamical models for a two-state variable on several topologies with increasing levels of heterogeneity in the degree distribution. We find that the zero-temperature Glauber dynamics for the Ising model may get trapped in sets of partially ordered metastable states even for finite system size, and this becomes more probable as the size increases. Voter dynamics instead always converges to full order on finite networks, even if this does not occur via coherent growth of domains. The time needed for order to be reached diverges with the system size. In both cases the ordering process is rather insensitive to the variation of the degreee distribution from sharply peaked to scale-free.