Order-disorder transitions in a minimal model of active elasticity

Abstract

We introduce a new minimal model for self-propelled agents that attract, repel, and align to their neighbors through elastic interactions. This model has a simple mechanical realization and provides an approximate description of real-world systems ranging from active cell membranes to robotic or animal groups with predictive capabilities. The agents are connected to their neighbors by linear springs attached at a distance R in front of their centers of rotation. For small R, the elastic interactions mainly produce attraction-repulsion forces between agents; for large R, they mainly produce alignment. We show that the agents self-organize into collective motion through an order-disorder noise-induced transition that is discontinuous for small R and continuous for large R in finite-size systems. In large-scale systems, only the discontinuous transition will survive, as long-range order decays for intermediate noise values. This is consistent with previous results where collective motion is driven either by attraction-repulsion or by alignment forces. For large R values and different parameter settings, the system displays a novel transition to a state of quenched disorder. In this regime, lines of opposing forces are formed that separate domains with different orientations and are stabilized by noise, producing locally ordered yet globally disordered quenched states.