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Theory of Hyperuniformity at the Absorbing State Transition

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arxiv 2310.17391 v1 pith:AZKZQUPC submitted 2023-10-26 cond-mat.stat-mech

Xiao Ma , Johannes Pausch , Michael E. Cates This is my paper · ORCID
classification cond-mat.stat-mech
keywords varsigmac-dpepsilonhyperuniformityabsorbingemergesexponentsfunctional
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abstract

Hyperuniformity, whereby the static structure factor (or density correlator) obeys $S(q)\sim q^{\varsigma}$ with $\varsigma> 0$, 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 $\varsigma$ are lacking. Specifically, $\varsigma$ 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 $\varsigma = 0^+$ and $\varsigma= 2\epsilon/9 + O(\epsilon^2)$ in dimension $d>4$ and $d=4-\epsilon$ respectively. The latter disproves a previously conjectured scaling relation for $\varsigma$. 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.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Self-organized hyperuniformity in a minimal model of population dynamics

    cond-mat.stat-mech 2025-09 conditional novelty 8.0 of 10

    A minimal population model with resource-based feedback self-tunes to a critical state and exhibits type-I hyperuniform density fluctuations, arising from divergent lifetimes rather than conservation laws.

  2. Hyperuniformity at the Absorbing State Transition: Perturbative RG for Random Organization

    cond-mat.stat-mech 2025-07 conditional novelty 8.0 of 10

    A one-loop perturbative RG calculation yields the hyperuniformity exponent ς=2ε/9 for random organization, distinct from the conserved directed percolation value ε/3.

  3. Yielding versus random organization: convex absorbing transitions in soft matter

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    Two soft matter models with long-range interactions both display convex absorbing transitions, crossing over from concave to convex regimes as interaction range increases, with critical exponents unified parametricall...

  4. Active Hyperuniform Networks of Chiral Magnetic Micro-Robotic Spinners

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    Magnetic micro-robotic spinners with three binding sites self-assemble into stable disordered hyperuniform networks at up to about a thousand robots.

  5. Ordinary Disordered Materials Can Carry Hyperuniform Physical Fields

    cond-mat.mtrl-sci 2026-07 conditional novelty 4.0 of 10

    Derivative-generated physical source fields (bound charge, bound current, incompatibility) are hyperuniform even when their parent fields are ordinary disordered noise.

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