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

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-α and we conjecture the exact value α=1/2, suggesting density fluctuations decay as r-3/2. We present a simple Gaussian field theory for the long-distance behavior of critical absorbing states and discuss implications for the Manna universality class.