Percolation and Criticality in Hyperuniform Networks

Hyperuniformity provides a general framework for studying point configurations with suppressed density fluctuations on macroscopic scales, encompassing both lattices and certain exotic disordered systems with quasi-long-range correlations. Percolation, in turn, is a classic continuous phase transition model in statistical physics that probes transport in disordered media. We study distance-based bond percolation on Delaunay triangulation networks derived from stealthy hyperuniform and Poisson (uncorrelated) point configurations. Using the Newman–Ziff Monte Carlo algorithm and finite-size scaling analysis, we estimate critical thresholds and exponents across a range of system sizes. Our results show clear differences between hyperuniform and Poisson embeddings: hyperuniform networks percolate more readily and display distinctive universality-class characteristics, with the stealthiness parameter providing a natural knob to tune the critical point. These findings suggest that hyperuniformity, beyond its structural definition, manifests as an emergent property in macroscopic critical phenomena. This perspective opens new pathways for designing network architectures with tailored transport properties, linking structural order, phase transitions, and applied network design.