Abstract
This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size-scaling ansatz for the time-dependent order parameter distribution function is proposed, and tested with extensive Monte-Carlo simulations of domain growth in the 2-D spin-flip kinetic Ising model. The scaling properties of the distribution functions serve to elucidate the configurational self-similarity that underlies the dynamic scaling picture. Moreover, it is demonstrated that the application of finite-size-scaling techniques facilitates the accurate determination of the bulk growth exponent even in the presence of strong finite-size effects, the scale and character of which are graphically exposed by the order parameter distribution function. In addition it is found that one commonly used measure of domain size-the scaled second moment of the magnetisation distribution-belies the full extent of these finite-size effects.
Similar content being viewed by others
References
Reviews of the field are given by Gunton, J.D., San Miguel, M., Sahni, P.S.: In: Phase transitions and critical phenomena, Vol. 8. Domb, C., Lebowitz, J.L. (eds.). New York: Academic Press 1983; Furukawa, H.: Adv. Phys.34, 703 (1985); Binder, K.: Rep. Prog. Phys.50, 783 (1987); Langer, J.S.: In: Solids far from equilibrium. Godreche, C. (ed.). Cambridge: Cambridge University Press 1992
Lifshitz, I.M.: Sov. Phys.-JETP15, 939 (1962)
Allen, S.M., Cahn, J.W.: Acta Metallus27, 1085 (1979)
Lifshitz, I.M., Slyozov, V.V.: J. Phys. Chem. Solids19, 35 (1961); Huse, D.A.: Phys. Rev. B34, 7845 (1986)
Bray, A.J.: Phys. Rev. B41, 6724 (1990)
Lai, Z.W., Mazenko, G.F., Valls, O.T.: Phys. Rev. B37, 9481 (1988)
Zhang, F.C., Valls, O.T., Mazenko, G.F.: Phys. Rev.B 31, 1579 (1985)
Mazenko, G.F.: Phys. Rev. B42, 4487 (1990)
Mazenko, G.F., Valls, O.T.: Phys. Rev. B27, 6811 (1983)
Roland, C., Grant, M.: Phys. Rev. B39, 11971 (1989)
Mazenko, G.F., Valls, O.T., Zhang, F.C.: Phys. Rev. B31, 4453 (1985)
Kumar, S., Viñals, J., Gunton, J.D.: Phys. Rev. B34, 1908 (1986)
Viñals, J., Jasnow, D.: Phys. Rev. B37, 9582 (1988)
Guo, H., Zheng, Q., Gunton, J.D.: Phys. Rev. B38, 11547 (1988)
Milchev, A., Binder, K., Heermann, D.W.: Z. Phys. B63, 521 (1986)
See for example Morris, D.G., Besag, F.M., Smallman, R.E.: Philos. Mag.29, 43 (1974); Noda, Y., Nishihara, S., Yamada, Y.: J. Phys. Soc. Jpn.53, 4241 (1984)
Gawlinski, E.T., Grant, M., Gunton, J.D., Kaski, K.: Phys. Rev. B31, 281 (1985)
Humayun, K., Bray, A.J.: J. Phys. A24, 1915 (1991)
Sadiq, A., Binder, K.: J. Stat. Phys.35, 517 (1984)
Fichthorn, K.A., Weinberg, W.H.: Phys. Rev. B46, 13702 (1992)
Kaski, K., Yalabik, M.C., Gunton, J.D., Sahni, P.S.: Phys. Rev.B 28, 5263 (1983)
Safran, S.A., Sahni, P.S., Grest, G.S.: Phys. Rev. B28, 2693 (1983)
Sahni, P.S., Grest, G.S., Safran, S.A.: Phys. Rev. Lett.50, 60 (1983); Grest, G.S., Safran, S.A., Sahni, P.S.: J. Chem. Phys.55, 2432 (1984)
Grant, M., Gunton, J.D.: Phys. Rev. B28, 5496 (1983)
Binder, K., Heermann, D.W.: Monte-Carlo simulation in statistical physics. 2nd edn. Berlin, Heidelberg, New York: Springer 1992
Gawlinski, E.T., Kumar, S., Grant, M., Gunton, J.D., Kaski, K.: Phys. Rev. B32, 1575 (1985)
Viñals, J., Grant, M.: Phys. Rev. B36, 7036 (1987)