Synchronous and Asynchronous Updates of Active Ising Spins in One Dimension

TL;DR

This paper investigates how different update rules, parallel and random-sequential, influence the dynamical behavior and phase transition nature of active Ising spins in one dimension, revealing significant differences in flock dynamics.

Contribution

It compares the effects of parallel and random-sequential update rules on the dynamical and phase transition properties of active Ising spins in one dimension.

Findings

Random-sequential updates increase directional switching.

Parallel updates lead to discontinuous phase transitions.

Random-sequential updates result in continuous phase transitions.

Abstract

How do update rules affect the dynamical and steady state properties of a flock? In this study, we have explored the active Ising spins (s = +-1) in one dimension, where spin updates its orientation according to the Metropolis algorithm (based on the neighbors) via two different update rules. (i) Parallel, and (ii) Random-sequential. We explore the effect of Parallel and Random-sequential updates on the dynamical properties of flocks in one dimension. Due to the inherent asynchronous nature of the Random-sequential update, the directional switching of the flock is increased compared to the Parallel one. The nature of phase transition is affected by the difference in the updating mechanism: discontinuous for Parallel and continuous for Random-sequential updates.