Inverse Ising inference, hyperuniformity and absorbing states in the Manna model

TL;DR

This paper uses inverse Ising inference to analyze the absorbing states of the one-dimensional Manna model, revealing an emergent equilibrium interaction with specific decay properties and implications for critical behavior and universality.

Contribution

It introduces an equilibrium model describing the absorbing states of the Manna model with emergent interactions and provides a Gaussian field theory for critical behavior.

Findings

Absorbing states exhibit short-ranged repulsion and long-ranged attraction.

Interaction becomes purely repulsive near the critical point, decaying as r^{-1/2}.

Density fluctuations decay as r^{-3/2}.

Abstract

Using inverse Ising inference we show that the absorbing states of the one-dimensional Manna model can be described by an equilibrium model with an emergent interaction displaying short-ranged repulsion and long-ranged attraction. As the model approaches the critical point the interaction becomes purely repulsive, decaying as $r^{-\alpha}$ and we conjecture the exact value $\alpha=1/2$, suggesting density fluctuations decay as $r^{-3/2}$. We present a simple Gaussian field theory for the long distance behaviour of critical absorbing states and discuss implications for the Manna universality class.