SciPost Submission Page

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

by Xiao Ma, Johannes Pausch, Gunnar Pruessner, Michael E. Cates

Submission summary

Abstract

Hyperuniformity, in which the static structure factor or density correlator obeys $S(q)\sim q^{\varsigma}$ with $\varsigma> 0$, emerges at criticality in systems having multiple, symmetry-unrelated, absorbing states. Important examples arise in periodically sheared suspensions and amorphous solids; these lie in the random organisation (RO) universality class. 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 $d>d_c=4$ and $d=4-\epsilon$ respectively. Our calculations assume that renormalizability is sustained via a certain pattern of cancellation of strongly divergent terms. These cancellations allow the upper critical dimension to remain $d_c = 4$, as is known to hold for RO, whereas generic perturbations ({\em e.g.}, those violating particle conservation) would typically flow to a fixed point with $d_c=6$. The assumed cancellation pattern is closely reminiscent of a long-established one near the tricritical Ising fixed point. (This has $d_c=3$, although generic perturbations flow instead towards the Wilson-Fisher fixed point with $d_c = 4$.) We show how hyperuniformity in RO emerges from anticorrelation of strongly fluctuating active and passive densities. Our one-loop calculations also yield the remaining RO exponents to order $\epsilon$, surprisingly without recourse to functional RG methods. These exponents coincide as expected with the Conserved Directed Percolation (C-DP) class which also contains the Manna Model and the quenched Edwards-Wilkinson (q-EW) model. Importantly however, our $\varsigma$ exponent differs from one found via a mapping to q-EW. In that mapping, $\varsigma$ is calculated by discarding an irrelevant conserved noise term. Here we argue that this term is {\em dangerously} irrelevant, allowing $\varsigma$ to change value. Thus, although other exponents are common to both, the RO and C-DP universality classes have different exponents for hyperuniformity.

Author indications on fulfilling journal expectations

• Provide a novel and synergetic link between different research areas.
• Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
• Detail a groundbreaking theoretical/experimental/computational discovery
• Present a breakthrough on a previously-identified and long-standing research stumbling block

Author comments upon resubmission