Active polar flock with birth and death

TL;DR

This paper investigates a lattice model of active polar particles with birth and death processes, revealing how these processes influence the nature of the disorder-to-order phase transition, transitioning from discontinuous to continuous as birth-death rates vary.

Contribution

The study introduces a minimal active Ising model incorporating birth and death, and analyzes how these processes affect phase transition characteristics.

Findings

Disorder-to-order transition changes from first order to continuous with increasing birth-death rate.

Effective free energy analysis confirms the transition nature dependence on birth-death rate.

System exhibits a crossover in phase transition behavior controlled by birth and death dynamics.

Abstract

We study a collection of self-propelled polar particles on a two-dimensional substrate with birth and death. We introduce a minimal lattice model for the system using active Ising spins, where each particle can have two possible orientations. The activity is modeled as a biased movement of the particle along its direction of orientation. The particles also align with their nearest neighbors using Metropolis Monte-Carlo algorithm. System shows a disorder-to-order transition by tuning the temperature of the system. Additionally, the birth and death of the particles is introduced through a birth and death rate $\gamma$. The system is studied near the disorder-to-order transition. The nature of disorder-to-order transition shows a crossover from first order, discontinuous to continuous type as we tune $\gamma$ from zero to finite values. We also write the effective free energy of the local order parameter using renormalised mean field theory and it confirms the dependence of the nature of phase transition on the birth and death rate parameter.