Metastable Hyperuniformity at Discontinuous Absorbing Transitions

TL;DR

This paper reveals that metastable hyperuniformity is a common structural feature near discontinuous absorbing transitions, characterized by anomalous scaling, and is explained by a minimal theoretical model involving nonlinear activation and conserved noise.

Contribution

It demonstrates the existence of metastable hyperuniform regimes at discontinuous absorbing transitions and provides a minimal field theory explaining its origin.

Findings

Metastable hyperuniformity appears only near the transition's stability limit.

Anomalous scaling $S(k o0) o k^{1.2}$ is observed in simulations.

The minimal theory reproduces the hyperuniform regime and scaling.

Abstract

Nonequilibrium hyperuniformity can arise either as a steady-state property of driven active fluids or as a critical signature at continuous absorbing transition points in two and three dimensions. Whether analogous structural order exists near discontinuous absorbing transitions, and what mechanism generates it, remains unclear. Here, we show that discontinuous absorbing transitions generically host a metastable hyperuniform regime near the stability limit. Using a facilitated Manna model without center-of-mass conservation, we find anomalous scaling $S(k\to0)\sim k^{1.2}$, which appears only near the metastable regime and disappears both deep in the active phase and in the absorbing phase. This scaling is robust in both two and three dimensions, in contrast to critical hyperuniformity at continuous absorbing transitions. We further formulate a minimal conserved Reggeon field theory that reproduces the same metastable hyperuniform regime and anomalous scaling, demonstrating that the phenomenon does not rely on microscopic update rules but arises from the interplay of nonlinear activation, multiplicative demographic noise, and conserved diffusive fluctuations. These results identify metastable hyperuniformity as a generic pseudo-critical structural signature of discontinuous absorbing transitions coupled to a conserved density.