# Phase transition in a one-dimensional Ising ferromagnet at zero-temperature under Glauber dynamics with a synchronous updating mode

## TL;DR

This paper investigates the phase transition behavior of a one-dimensional Ising ferromagnet under zero-temperature Glauber dynamics with synchronous updating, revealing a discontinuous transition between ferromagnetic and antiferromagnetic phases.

## Contribution

It introduces a generalized class of zero-temperature Glauber dynamics and demonstrates a discontinuous phase transition using Monte Carlo simulations and mean field analysis.

## Key findings

- Discontinuous phase transition between ferromagnetic and antiferromagnetic phases.
- Synchronous updating influences the steady state of the system.
- Monte Carlo simulations confirm the phase transition.

## Abstract

In the past decade low-temperature Glauber dynamics for the one-dimensional Ising system has been several times observed experimentally and occurred to be one of the most important theoretical approaches in a field of molecular nanomagnets. On the other hand, it has been shown recently that Glauber dynamics with the Metropolis flipping probability for the zero-temperature Ising ferromagnet under synchronous updating can lead surprisingly to the antiferromagnetic steady state. In this paper the generalized class of Glauber dynamics at zero-temperature will be considered and the relaxation into the ground state, after a quench from high temperature, will be investigated. Using Monte Carlo simulations and a mean field approach, discontinuous phase transition between ferromagnetic and antiferromagnetic phases for a one-dimensional ferromagnet will be shown.