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

BK21 Physics Research Division and Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea

^*beomjun@skku.edu

Phys. Rev. E 83, 033101 – Published 3 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.033101

Abstract

Sznajd-Weron [Phys. Rev. E 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 that the phase transition instead is of a continuous nature, and we identify critical exponents, $β \approx 0$ , $ν \approx 1$ , and $z \approx 2$ , via a systematic finite-size scaling analysis.

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References (3)

K. Sznajd-Weron, Phys. Rev. E 82, 031120 (2010).
N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, Boston, 1992).
Although not shown here, we have confirmed that the magnetization and its Binder’s cumulant, the staggered magnetization and its Binder’s cumulant, and the Binder’s cumulant for $ρ_{st}$ all show good quality of finite-size scalings with the values $W_{c} = 0.5$ , $β = 0$ , and $ν = 1$ .

Physical Review E

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

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

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