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.

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.