Hyperuniformity in the Manna Model, Conserved Directed Percolation and Depinning
Kay Jörg Wiese1
1CNRS-Laboratoire de Physique de
l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Universités, Université Paris-Diderot, Sorbonne Paris Cité
24 rue Lhomond, 75005 Paris, France
Abstract
We use an exact mapping of the Manna model, or equivalently
conserved directed percolation, onto disordered elastic manifolds at depinning to show that particle-density fluctuations in these two models are hyperuniform. The structure factor of the particle density behaves for small $q$ as $S(q)\sim |q|^\sigma$ with $\sigma={4-d-2\zeta}$, where $\zeta$ is the roughness exponent at depinning.
In dimension $d=1$, $\sigma=1/2$, while for all dimensions $0.6> \sigma\ge0$. Our results fit well known simulations in the literature, except in $d=1$, where we perform our own simulations to confirm our findings.
arXiv:2401.09123 [pdf]
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by Kay Wiese. Last edited January 20, 2024.