Do topological perturbations trigger dimensional phase transitions in networks?

Determine whether topological perturbations—specifically shortcut addition via rewiring and link removal (dilution)—can induce genuine structural phase transitions in the spectral dimension of lattices and complex networks, as defined through the Laplacian Renormalization Group framework.

Background

The paper studies scale-invariant networks using the Laplacian Renormalization Group (LRG), where the heat capacity plateau encodes the spectral dimension ds. The authors ask whether structural perturbations like adding shortcuts or deleting links can cause true phase transitions in this dimension, rather than smooth crossovers.

This question is central to understanding how quenched disorder and small-world effects reconfigure the large-scale geometry and universality classes of networks, potentially leading to new structural fixed points and attraction basins.