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Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributions

Author

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  • Alves, Sidiney G.
  • Ferreira, Silvio C.
  • de Oliveira, Marcelo M.

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)∼q−α with exponent α≈5.6, and a square lattice. We analyze the role of the disorder in the modified WPS model, considering the critical behavior of the contact process (CP). 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 ω=1/2, the disorder effects observed for the WPS lattice are weaker than those found for uncorrelated disorder.

Suggested Citation

  • Alves, Sidiney G. & Ferreira, Silvio C. & de Oliveira, Marcelo M., 2024. "Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 652(C).
    • Handle: RePEc:eee:phsmap:v:652:y:2024:i:c:s0378437124005569
    DOI: 10.1016/j.physa.2024.130047
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