Role of Random Interaction Connection in the Order Transition of Active Matter Based on the Vicsek Model

TL;DR

This paper investigates how introducing randomness in interaction connections affects the order transition in active matter modeled by the Vicsek model, revealing a first-order phase transition influenced by the perception rate P.

Contribution

It explicitly incorporates perception rate P into the Vicsek model, modeling interaction connections as superposition states, and analyzes their impact on phase transition and network structure.

Findings

Order transition is a first-order phase transition with band formation.

Increasing P leads to order saturation and phase separation.

Network analysis shows robustness against random edge removal.

Abstract

Randomness plays a key role in the order transition of active matter but has not yet been explicitly considered in pairwise interaction connection. In this letter, we introduce the perception rate P into the Vicsek model as the probability of the interaction connections and model the connections as superposition states. We show that with increasing P, the polar order number undergoes an order transition and then saturation. The order transition is a first-order phase transition with band formation, and the effect of P is different from density. The change of the order number is linked with the interaction structure. The order transition, order saturation, and phase separation correspond to different critical changes in the local interaction number. The global interaction structure is further analyzed as a network. The decrease of P is comparable to random edge removal, under which the network experiences modal transitions near the critical points of the order number, and the network exhibits surprising robustness. Our results suggest that random interaction can be a new important factor in active matter models, with potential applications in robotic swarms and social activities.