Wiese Kay Jörg
CNRS-Laboratoire de Physique de <a href="https://ror.org/05a0dhs15">l'Ecole Normale Supérieure</a>, PSL Research University, <a href="https://ror.org/02en5vm52">Sorbonne Université</a>, Université Paris Cité, 24 rue Lhomond, 75005 Paris, France.
Phys Rev Lett. 2024 Aug 9;133(6):067103. doi: 10.1103/PhysRevLett.133.067103.
Hyperuniformity is an emergent property, whereby the structure factor of the density n scales as S(q)∼q^{α}, with α>0. We show that for the conserved directed percolation (CDP) class, to which the Manna model belongs, there is an exact mapping between the density n in CDP, and the interface position u at depinning, n(x)=n_{0}+∇^{2}u(x), where n_{0} is the conserved particle density. As a consequence, the hyperuniformity exponent equals α=4-d-2ζ, with ζ the roughness exponent at depinning, and d the dimension. In d=1, α=1/2, while 0.6>α≥0 for other d. Our results fit well the simulations in the literature, except in d=1, where we perform our own to confirm this result. Such an exact relation between two seemingly different fields is surprising, and paves new paths to think about hyperuniformity and depinning. As corollaries, we get results of unprecedented precision in all dimensions, exact in d=1. This corrects earlier work on hyperuniformity in CDP.
超均匀性是一种涌现性质，密度(n)的结构因子按(S(q)∼q^{α})缩放，其中(α>0)。我们表明，对于曼纳模型所属的守恒定向渗流（CDP）类，CDP中的密度(n)与脱钉时的界面位置(u)之间存在精确映射，(n(x)=n_{0}+∇^{2}u(x))，其中(n_{0})是守恒粒子密度。因此，超均匀性指数等于(α=4 - d - 2ζ)，其中(ζ)是脱钉时的粗糙度指数，(d)是维度。在(d = 1)时，(α = 1/2)，而在其他维度(0.6>α≥0)。我们的结果与文献中的模拟结果非常吻合，除了在(d = 1)时，我们自己进行了模拟以证实这一结果。两个看似不同的领域之间存在这样一种精确关系令人惊讶，并为思考超均匀性和脱钉开辟了新途径。作为推论，我们在所有维度上都得到了前所未有的精度结果，在(d = 1)时是精确的。这纠正了早期关于CDP中超均匀性的工作。
