Ordering kinetics of two-dimensional O(2) models: Scaling and temperature dependence

Jong-Rim Lee; Sung Jong Lee; Bongsoo Kim

doi:10.1103/PhysRevE.52.1550

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Ordering kinetics of two-dimensional O(2) models: Scaling and temperature dependence

Jong-Rim Lee, Sung Jong Lee, and Bongsoo Kim

Center for Theoretical Physics, Seoul National University, Seoul 151-742 Korea
Department of Physics, Changwon National University, Changwon, 641-773, Korea

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Phys. Rev. E 52, 1550 – Published 1 August, 1995

DOI: https://doi.org/10.1103/PhysRevE.52.1550

Abstract

This paper presents simulation results on the phase-ordering kinetics of two-dimensional O(2) models. Both the time-dependent Ginzburg-Landau (TDGL) model and the fixed length spin XY model on a square lattice are studied using the Langevin dynamics approach. The equal-time correlation functions of the TDGL model at zero temperature quench are shown to scale best with the length scale form of L(t)∼[t/(lnt $)^{γ}$ $]^{0.5}$ , with γ≃0.7, which is also consistent with the length scale derived from the energy-scaling argument, although with a slightly different value of γ. Critical dynamic scaling is satisfied for quenches to finite temperatures below $T_{KT}$ (the Kosterlitz-Thouless transition temperature). Autocorrelation functions show reasonable agreement with the theoretically predicted behavior of A(t)∼L(t $)_{0}^{- [λ}$ +η(T)], where $λ_{0}$ is the zero temperature exponent for the autocorrelation and η(T) is the temperature-dependent exponent for the equilibrium correlation function.

References (24)

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[c1] J. D. Gunton, M. San Miguel, and P. S. Sahni, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, New York, 1983), Vol 8; H. Furukawa, Adv. Phys. 34, 703 (1985); K. Binder, Rep. Prog. Theor. Phys. 50, 783 (1987).

[c2] G. F. Mazenko and M. Zannetti, Phys. Rev. Lett. 53, 2106 (1984); Phys. Rev. B 32, 4565 (1985) ibid. 35, 4565 (1987).

[c3] F. de Pasquale and P. Tartaglia, Phys. Rev. B 33, 2081 (1986); F. de Pasquale, G. F. Mazenko, P. Tartaglia and M. Zannetti, ibid. 37, 296 (1988).

[c4] A. J. Bray and S. Puri, Phys. Rev. Lett. 67, 2670 (1991).

[c5] F. Liu and G. F. Mazenko, Phys. Rev. B 45, 6989 (1992), and references therein.

[c6] H. Toyoki, Phys. Rev. B 45, 1965 (1992).

[c7] A. J. Bray, in Phase Transitions in Systems with Competing Energy Scales, edited by T. Riste and D. Sherrington (Kluwer Academic, Boston, 1993).

[c8] R. Loft and T. A. Degrand, Phys. Rev. B 35, 8528 (1987).

[c9] H. Toyoki and K. Honda, Prog. Theor. Phys. 78, 237 (1987).

[c10] M. Mondello and N. Goldenfeld, Phys. Rev. A 42, 5865 (1990); ibid. 47, 2384 (1993).

[c11] A. J. Bray and K. Humayun, J. Phys. A 23, 5897 (1990).

[c12] S. Puri and C. Roland, Phys. Lett. A 151, 500 (1990).

[c13] H. Toyoki, Phys. Rev. A 42, 911 (1990).

[c14] B. Yurke, A. N. Pargellis, T. Kovacs and D. A. Huse, Phys. Rev. E 47, 1525 (1993).

[c15] R. E. Blundell and A. J. Bray, Phys. Rev. E 49, 4925 (1994).

[c16] J. M. Kosterlitz and D. Thouless, J. Phys. C 6, 1181 (1973); J. M. Kosterlitz, ibid. 7, 1046 (1974).

[c17] S. J. Lee, J. R. Lee and B. Kim, Phys. Rev. E 51, R4 (1995).

[c18] A. J. Bray and A. D. Rutenberg, Phys. Rev. E 49, R27 (1994); A. D. Rutenberg and A. J. Bray (unpublished).

[c19] A. J. Bray and K. Humayun, Phys. Rev. E 47, R9 (1993).

[c20] D. S. Fisher and D.A. Huse, Phys. Rev. B 38, 373 (1988); D. A. Huse, ibid. 40, 304 (1989).

[c21] A. A. Ovchinnikov and Ya. B. Zeldovich, Chem. Phys. 28, 214 (1978); D. Toussaint and F. Wilczek, J. Chem. Phys. 78, 2642 (1983); K. Kang and S. Redner, Phys. Rev. A 30, 2833 (1984).

[c22] F. Liu, Phys. Rev. E 48, 2422 (1993).

[c23] T. J. Newman and A. J. Bray, J. Phys. A 23, L279 (1990); ibid. 23, 4491 (1990).

[c24] J. Villain, J. Phys. (Paris) 36, 581 (1973).

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Ordering kinetics of two-dimensional O(2) models: Scaling and temperature dependence

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