Comment on "Phase transition in a one-dimensional Ising ferromagnet at zero temperature using Glauber dynamics with a synchronous updating mode"

TL;DR

This paper challenges previous claims by demonstrating that the phase transition in a one-dimensional Ising model with zero temperature synchronous Glauber dynamics is continuous, providing critical exponents through finite-size scaling analysis.

Contribution

It corrects the earlier assertion of a discontinuous transition, establishing the transition as continuous and identifying its critical exponents.

Findings

The phase transition is continuous, not discontinuous.

Critical exponents are approximately β=0, ν=1, z=2.

Finite-size scaling analysis supports the continuous transition conclusion.

Abstract

Sznajd-Weron in [Phys. Rev. E {\bf 82}, 031120 (2010)] suggested that the one-dimensional Ising model subject to the zero temperature synchronous Glauber dynamics exhibits a discontinuous phase transition. We show here instead that the phase transition is of a continuous nature and identify critical exponents: $\beta \approx 0$, $\nu \approx 1$, and $z \approx 2$, via a systematic finite-size scaling analysis.