Anomalous Criticality of Absorbing State Transition toward Jamming

TL;DR

The paper questions the direct mapping of jamming-criticality to the Manna universality class by reexamining the biased random organization (BRO) model at high density. It identifies three main phenomena: (i) crystallization in 3D monodisperse systems interrupts the absorbing transition, (ii) an absorbing-to-active-glass universality with distinct exponents appears in dense binary mixtures, and (iii) Griffiths effects near jamming smear the dynamic transition, yielding a pseudo-critical regime; in the near-jamming limit ($\varepsilon \to 0$) the BRO dynamics map to directed percolation on a heterogeneous network. A field theory with fractional time dynamics is proposed to unify absorbing-to-active-glass transitions and heterogeneous DP, linking jamming, disorder, and dynamic criticality. These findings broaden the understanding of dynamic criticality in disordered, high-density systems and point to connections with glassy physics and neural-network-like learning processes. $\varphi_c$, $\varepsilon$, $t^*$, $z^*$, $\nu_{\perp}$, and $\nu_{\parallel}$ are central to the reported scaling analyses, while fractional-time dynamics distinguish the observed regimes from the conventional Manna universality.

Abstract

The jamming transition is traditionally regarded as a geometric transition governed by static contact networks. Recently, dynamic phase transitions of athermal particles under periodic shear provide a new lens on this problem, leading to a conjecture that jamming transition corresponds to an absorbing-state transition within the Manna (conserved directed percolation) universality class. Here, by re-examining the biased random organization model, a minimal model for particles under periodic shearing that the conjecture is based on, we uncover several criticality anomalies at high density at odds with Manna universality class. In three-dimensional monodisperse systems, we find crystallization disrupts the absorbing transition, while in dense binary mixtures, a distinct transition from absorbing to active-glass states emerges, signifying a new universality class of dynamic phase transition. Closer to the jamming point, the quenched heterogeneity in the contact network smears the dynamic transition via Griffiths effects and drives the system toward heterogeneous directed percolation. We propose a field theory with fractional time dynamics that unifies these phenomena, establishing a theoretical framework linking jamming, disorder, and dynamic criticality.

Figures (4)

• Figure 1: (a) Schematic of the BRO model: overlapping particles (red) become active and take pairwise repulsive displacements. (b) $f_a^{\infty}$ as a function of packing fraction $\varphi$ at $\varepsilon=2.0~\sigma$. (c) Evolution of $f_b(t)$ for systems at $\varepsilon=2.0~\sigma$ under various $\varphi$. The dashed line represents the power law $t^{-0.45}$. Here $N=65536$. (d) Critical packing fractions $\varphi_c$ for 2D binary (red line), 3D binary (orange dots), 3D monodisperse (blue circles) and 4D monodisperse (green open squares) systems at different $\varepsilon$. Asterisks mark the extrapolated $\varphi_c$ for $\varepsilon \rightarrow 0$, i.e., 0.840 (2D) and 0.638 (3D) and 0.455 (4D), which is consistent with the RCP.
• Figure 2: (a, d) Finite size scaling for survival activity $f_a(t)$ and survival probability $P_s(t)$ at $\varepsilon=0.8\sigma$, $\varphi_c=0.6324$, from which we obtain $\alpha=0.21,z=2.75$. (b, e) Finite size scaling for $f_a^{\infty}$ and $t^*$ at $\varepsilon=0.8\sigma$. (c, f) Critical exponents of $\beta$, $\nu_{\parallel}$, $\alpha$, $z$ as functions of $\varepsilon$, from which one can distinguish three regimes, I, II, III. Red and blue dotted lines represent the value of $\alpha, z, \nu_{\parallel}, \beta$ in the Manna universality. (g, h) MSD(t) for systems with $\varepsilon=1.5\sigma$ (g) and $\varepsilon=0.5\sigma$ (h), where the open/solid symbols represent the absorbing/active state. (i) Diffusion coefficients $D$ (solid line) and $f_a^{\infty}$ (dotted line) as functions of $\varphi$ at various $\varepsilon$.
• Figure 3: (a, e) Evolution of $f_b(t)$ at different $\varphi$, where Griffiths regime is painted in gray. (b, f) Evolution of $f_b(t)$ at different $N$. And $\varphi=0.8128$(upper) and $0.4920$ (lower). (c, g) Relationship between index $\kappa$ and $\varphi$. (d, h) Distributions of normalized activity duration $f_{ad}$ at $\varphi=0.7838, \varepsilon=0.2\sigma$(upper) and $0.4980, \varepsilon=1.5\sigma$, $\Delta \varepsilon = 1.2 \sigma$, $l=1\sigma$ (lower). (a, b) are for the original BRO model with $\varepsilon=0.1\sigma$. (e, f) are for modified BRO models with quenched-disorder at $\varepsilon=1.5\sigma$, $\Delta \varepsilon = 1.2 \sigma$ and $l=2\sigma$. For all systems except (b,f), $N=8192$.
• Figure 4: (a, c) Finite size effects of survival probability of dynamic trajectory $P_s(t)$. (d, f) Distributions of normalized activity duration. (a, b) are for the original BRO models near the transition point at $\varepsilon=0.01\sigma$ and $\varphi=0.8380$. (c, d) are for the heterogeneous contact model at $P_e=0.788$ and $k=1$ based on the same configuration as in (b).