Nonequilibrium critical dynamics of the ferromagnetic Ising chain subject to slow cooling: Kawasaki’s spin-exchange kinetics

• Published in: Journal of the Korean Physical Society Vol. 81; no. 8; pp. 722 - 732
• Main Authors: Kim, Heejeong, Jeong, Kangeun, Kim, Bongsoo, Lee, Sung Jong
• Format: Journal Article
• Language: English
• Published: Seoul The Korean Physical Society 01.10.2022; Springer Nature B.V
• Subjects: Chains; Cooling; Exchanging; Ferromagnetism; Ising model; Kinetics; Mathematical and Computational Physics; Mathematical and Statistical Physics; Order parameters; Original Paper - General; Particle and Nuclear Physics; Physics; Physics and Astronomy; Spin dynamics; Theoretical; Slow cooling; Spin-exchange kinetic Ising model; Kibble–Zurek mechanism; Conserved order-parameter
• ISSN: 0374-4884; 1976-8524
• DOI: 10.1007/s40042-022-00614-8

We numerically investigate the nonequilibrium dynamics of the kinetic Ising chain under slow cooling to zero temperature, employing a spin-exchange kinetics that conserves the order parameter. We focus on a logarithmic cooling protocol with a tuning parameter. Applying the Kibble–Zurek mechanism to the considered cooling protocol, we derive the common expressions for the growing length and timescales with cooling, which holds for both the spin-flip and spin-exchange kinetics. The dynamic scaling behaviors of the excess defect density and spin correlation function indicate that the nonequilibrium dynamics is governed by the time and length scales that are in agreement with the predictions of the Kibble–Zurek mechanism. We find that the equal-time spatial spin correlation function at zero temperature exhibits a universal power law decay at long distance. At variance with an interesting possibility recently raised for the present system, no new length scale is found that is distinct from the Kibble–Zurek one. The measured correlation length exhibits an extraordinarily rapid growth process during the cooling down to zero temperature after the onset of nonequilibrium regime.