On the influence of long-ranged interactions on absorbing state phase transitions*

While the role of local interactions in non-equilibrium phase transitions is well studied, a fundamental understanding of the effects of long-range interactions is lacking. In particular, most attention was paid to systems where the long-ranged nature results from the underlying network structure. In our work, we study the critical dynamics of reproducing agents subject to long-ranged chemical interactions and limited resources. We emphasize the importance of the agent's diffusion speed relative to the diffusion speed of the signalling substance. In the limit of fast signal transduction, which gives rise to a Coulomb-like interaction, renormalization group analysis reveals distinct scaling regimes for attractive or repulsive interactions. In the limit of slow signal transduction the dynamics is dominated by a diffusive fixed point. Further, we suggest a novel nonlinear mechanism that stabilizes the continuous transition against the emergence of a characteristic length scale due to a chemotactic collapse.