Hyperuniformity in the Manna Model, Conserved Directed Percolation and Depinning

Kay Joerg Wiese

Published 2024-01-17Version 1

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.