Theory of Hyperuniformity at the Absorbing State Transition

Abstract

Hyperuniformity, whereby the static structure factor (or density correlator) obeys $S(q)\sim q^ς$ with $ς> 0$, emerges at criticality in systems having multiple absorbing states, such as periodically sheared suspensions. These lie in the conserved directed percolation (C-DP) universality class, for which analytic results for $ς$ are lacking. Specifically, $ς$ appears inaccessible within an exact `interfacial mapping' that yields other C-DP exponents via functional renormalization group (FRG). Here, using Doi-Peliti field theory for interacting particles and perturbative RG about a Gaussian model, we find $ς= 0^+$ and $ς= 2ε/9 + O(ε^2)$ in dimension $d>4$ and $d=4-ε$ respectively. The latter disproves a previously conjectured scaling relation for $ς$. We show how hyperuniformity emerges from anticorrelation of strongly fluctuating active and passive densities. Our calculations also yield the remaining C-DP exponents without recourse to functional RG methods.