Phase diagram for a zero-temperature Glauber dynamics under partially synchronous updates

TL;DR

This paper investigates the phase behavior of a one-dimensional zero-temperature Glauber dynamics system under partially synchronous updates, revealing a phase transition between ferromagnetic and active antiferromagnetic phases through simulations and analytical methods.

Contribution

It introduces a detailed phase diagram for partially synchronous Glauber dynamics and analytically explains the origin of the phase transition, extending previous work on synchronous updates.

Findings

Identifies a phase transition between ferromagnetic and active antiferromagnetic phases.

Provides analytical understanding of the phase transition mechanism.

Confirms simulation results with theoretical calculations.

Abstract

We consider generalized zero-temperature Glauber dynamics under partially synchronous updating mode for a one dimensional system. Using Monte Carlo simulations, we calculate the phase diagram and show that the system exhibits phase transition between ferromagnetic and active antiferromagnetic phase. Moreover, we provide analytical calculations that allow to understand the origin of the phase transition and confirm simulation results obtained earlier for synchronous updates.