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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.10095 |
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| _version_ | 1866909295546728448 |
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| author | Alves, Sidiney G. Ferreira, Silvio C. de Oliveira, Marcelo M. |
| author_facet | Alves, Sidiney G. Ferreira, Silvio C. de Oliveira, Marcelo M. |
| contents | 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, $P(q)\sim q^{-α}$ with exponent $α\approx 5.6$, 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 $ω=1/2$, the disorder effects observed for the WPS lattice are weaker than those found for uncorrelated disorder. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10095 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributions Alves, Sidiney G. Ferreira, Silvio C. de Oliveira, Marcelo M. Statistical Mechanics 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, $P(q)\sim q^{-α}$ with exponent $α\approx 5.6$, 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 $ω=1/2$, the disorder effects observed for the WPS lattice are weaker than those found for uncorrelated disorder. |
| title | Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2405.10095 |