Slow dynamics and rare-region effects in the contact process on weighted tree networks

TL;DR

This paper demonstrates that complex tree networks with weighted edges can exhibit slow, smeared phase transitions in the contact process due to rare-region effects, without external disorder.

Contribution

It reveals that topological features and weight patterns alone can induce slow dynamics and smeared transitions in the contact process on networks.

Findings

Slow dynamics arise from rare-region effects on correlated subspaces.

Weighted tree networks can produce smeared phase transitions.

Topological disorder may lead to Griffiths phases in networks.

Abstract

We show that generic, slow dynamics can occur in the contact process on complex networks with a tree-like structure and a superimposed weight pattern, in the absence of additional (non-topological) sources of quenched disorder. The slow dynamics is induced by rare-region effects occurring on correlated subspaces of vertices connected by large weight edges, and manifests in the form of a smeared phase transition. We conjecture that more sophisticated network motifs could be able to induce Griffiths phases, as a consequence of purely topological disorder.