An Absorbing State Model with an Emergent Ising Transition

Abstract

We study a dynamical model of repulsive needles with centers fixed on a square lattice. Needles that overlap are active and receive a repulsive rotation $\theta \in [0,\epsilon )$; needles with no overlap do not move. This model exhibits an absorbing state transition. Nematic order was observed for long needles. For a range of needle lengths and $\epsilon$, the system self-organizes into a state with checkerboard symmetry. As $\epsilon$ is increased, this phase melts and becomes disordered. Remarkably, we find that this phase boundary exhibits critical exponents identical to those of the equilibrium 2D Ising model.