Emergent complex phases in a discrete flocking model with reciprocal and non-reciprocal interactions

TL;DR

This paper investigates a two-species active Ising model with reciprocal and non-reciprocal interactions, revealing novel flocking states, complex phase diagrams, and validating findings with hydrodynamic theory.

Contribution

It introduces the discrete two-species active Ising model and uncovers new flocking phases and dynamics not previously observed in similar models.

Findings

High-density parallel flocking state in reciprocal interactions

Rich phase diagrams with interconversion dynamics

Run-and-chase behavior in non-reciprocal interactions

Abstract

There is growing interest in multi-species active matter systems with reciprocal and non-reciprocal interactions. While such interactions have been explored in continuous symmetry models, less is known about multi-species discrete-symmetry systems. To address this, we study the two-species active Ising model (TSAIM), a discrete counterpart of the two-species Vicsek model. Our investigation explores both inter-species reciprocal and non-reciprocal interactions, along with the possibility of species interconversion. In the reciprocal TSAIM, we observe the emergence of a high-density parallel flocking state, a feature not seen in previous flocking models. With species interconversion, the TSAIM corresponds to an active extension of the Ashkin-Teller model and exhibits rich state diagrams. In the non-reciprocal TSAIM, a run-and-chase dynamics emerge. We also find that the system is metastable due to droplet excitation and exhibits spontaneous motility-induced interface pinning. A hydrodynamic theory validates our numerical simulations and confirms the phase diagrams.