Hyperuniformity at the Absorbing State Transition: Perturbative RG for Random Organization
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2025
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| author | Ma, Xiao Pausch, Johannes Pruessner, Gunnar Cates, Michael E. |
| author_facet | Ma, Xiao Pausch, Johannes Pruessner, Gunnar Cates, Michael E. |
| contents | Hyperuniformity, where the static structure factor obeys $S(q)\sim q^ς$ with $ς> 0$, 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, for which analytic results for $ς$ are lacking. Here, using Doi-Peliti field theory and perturbative RG about a Gaussian model, we find $ς= 0^+$ and $ς= 2ε/9 + O(ε^2)$ in dimension $d>d_c=4$ and $d=4-ε$ 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 for RO, while generic perturbations (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 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 calculations also yield the remaining exponents to order $ε$, surprisingly without recourse to functional RG. 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 $ς$ differs from one found via a mapping to q-EW. That mapping neglects a conserved noise in the RO action, which we argue to be dangerously irrelevant. Thus, although other exponents are common to both, the RO and C-DP universality classes have different exponents for hyperuniformity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_07793 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperuniformity at the Absorbing State Transition: Perturbative RG for Random Organization Ma, Xiao Pausch, Johannes Pruessner, Gunnar Cates, Michael E. Statistical Mechanics Hyperuniformity, where the static structure factor obeys $S(q)\sim q^ς$ with $ς> 0$, 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, for which analytic results for $ς$ are lacking. Here, using Doi-Peliti field theory and perturbative RG about a Gaussian model, we find $ς= 0^+$ and $ς= 2ε/9 + O(ε^2)$ in dimension $d>d_c=4$ and $d=4-ε$ 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 for RO, while generic perturbations (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 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 calculations also yield the remaining exponents to order $ε$, surprisingly without recourse to functional RG. 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 $ς$ differs from one found via a mapping to q-EW. That mapping neglects a conserved noise in the RO action, which we argue to be dangerously irrelevant. Thus, although other exponents are common to both, the RO and C-DP universality classes have different exponents for hyperuniformity. |
| title | Hyperuniformity at the Absorbing State Transition: Perturbative RG for Random Organization |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2507.07793 |