Nonequilibrium kinetics of excess defect generation and dynamic scaling in the Ising spin chain under slow cooling

Kangeun Jeong, Bongsoo Kim, and Sung Jong Lee
Phys. Rev. E 102, 012114 – Published 6 July 2020

Abstract

We investigate the relaxation dynamics of a one-dimensional Ising chain via Glauber kinetic Monte Carlo simulations, when the system is cooled slowly from infinite temperature to zero temperature with different cooling protocols. The main quantity of interest is the excess defect density that represents the total defect density minus the equilibrium defect density at varying temperatures. We find that, for three classes of cooling protocols, the time dependence of the excess defect density for various cooling speed shows a dynamic scaling behavior that largely encompasses the Kibble-Zurek mechanism as well as Krapivsky's calculation of the final defect density at zero temperature. We also find distinct features in the behavior of the dynamic scaling when the temperature approaches in a power-law fashion to zero temperature and the excess defect density reaches a peak at finite temperature, where the scaling of the excess defect density at its peak and that at zero temperature exhibits different asymptotic behavior due to different logarithmic corrections. This characteristic behavior can be attributed to the exponential divergence of the relaxation time near zero temperature. While the qualitative theoretical predictions by Krapivsky on the asymptotic exponents are confirmed, the asymptotic predictions for amplitudes overestimate by up to 40% the simulation results.

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  • Received 25 March 2020
  • Accepted 17 June 2020

DOI:https://doi.org/10.1103/PhysRevE.102.012114

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Kangeun Jeong1, Bongsoo Kim1,2,*, and Sung Jong Lee2,3

  • 1Department of Physics, Changwon National University, Changwon 51140, Korea
  • 2Institute for Soft and Bio Matter Science, Changwon National University, Changwon 51140, Korea
  • 3Research Institute for Basic Sciences, Changwon National University, Changwon 51140, Korea

  • *bskim@changwon.ac.kr

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Vol. 102, Iss. 1 — July 2020

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