# Band structure in collective motion with quenched range of interaction

## TL;DR

This paper investigates a modified Vicsek model with spatially quenched, non-overlapping interaction ranges, revealing complex band formations and phase transitions in collective motion.

## Contribution

It introduces a novel interaction scheme based on discretized space, leading to new types of bands and phenomena not seen in the original Vicsek model.

## Key findings

- Discontinuous transition from diffusive to ordered phase at critical noise.
- Observation of various band types with different orientations and wrapping.
- Detection of crossed, independently moving band sets.

## Abstract

A variant of the well known Vicsek model of the collective motion of a group of agents has been studied where the range of interactions are spatially quenched and non-overlapping. To define such interactions, the underlying two dimensional space is discretized and is divided into the primitive cells of an imaginary square lattice. At any arbitrary time instant, all agents within one cell mutually interact with one another. Therefore, when an agent crosses the boundary of a cell, and moves to a neighboring cell, only then its influence is spread to the adjacent cell. Tuning the strength of the scalar noise $\eta$ it has been observed that the system makes a discontinuous transition from a random diffusive phase to an ordered phase through a critical noise strength $\eta_c$ where directed bands with high agent densities appear. Unlike the original Vicsek model here a host of different types of bands has been observed with different angles of orientation and different wrapping numbers. More interestingly, two mutually crossed independent sets of simultaneously moving bands are also observed. A prescription for the detailed characterization of different types of bands have been formulated.