Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributions

TL;DR

This paper investigates how topological disorder in planar random lattices with heterogeneous degree distributions affects critical dynamics, revealing nonuniversal scaling behaviors and weaker disorder effects than uncorrelated models.

Contribution

It introduces a modified WPS lattice model with tunable degree distributions and analyzes its impact on critical contact process dynamics, highlighting nonuniversal scaling and disorder relevance.

Findings

Critical scaling depends on degree distribution

Scaling exponents differ from mean-field predictions

Disorder effects are weaker than in uncorrelated models

Abstract

The weighted planar stochastic (WPS) lattice introduces a topological disorder that emerges from a multifractal structure. Its dual network has a power-law degree distribution and is embedded in a two-dimensional space, forming a planar network. We modify the original recipe to construct WPS networks with degree distributions interpolating smoothly between the original power-law tail, $P(q)\sim q^{-\alpha}$ with exponent $\alpha\approx 5.6$, and a square lattice. We analyze the role of disorder in the modified WPS model, considering the critical behavior of the contact process. We report a critical scaling depending on the network degree distribution. The scaling exponents differ from the standard mean-field behavior reported for CP on infinite-dimensional (random) graphs with power-law degree distribution. Furthermore, the disorder present in the WPS lattice model is in agreement with the Luck-Harris criterion for the relevance of disorder in critical dynamics. However, despite the same wandering exponent $\omega=1/2$, the disorder effects observed for the WPS lattice are weaker than those found for uncorrelated disorder.