Skip to main content
Log in

Global symmetry breaking in the nonconserved order parameter system during phase ordering

  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

We study global symmetry breaking in the 2D system of scalar nonconserved order parameter following a quench to zero temperature. We show that the instant of time when the symmetry is broken and the final morphology is chosen corresponds to the saturation of the order parameter inside the domains. There are three possible final morphologies: the positive and negative order parameter final morphology, and the state of the coexisting positive and negative order parameter subsystems with a flat interface between them. We find also that each type of the final morphology constitutes about 1/3 of all cases, what agrees with the results obtained recently by Spirin et al. [Phys. Rev. E 65, 016119 (2001)]. Our results are pertinent for the two dimensional systems, but we suspect that there is also a way to apply similar arguments for the three dimensional ones.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R.B. Laughlin, D. Pines, Proc. Natl. Acad. Sci. 97, 28 (2000)

    Google Scholar 

  2. R.B. Laughlin, D. Pines, J. Schmalian, B.P. Stojkovic, P. Wolynes, Proc. Natl. Acad. Sci. 97, 32 (2000)

    Google Scholar 

  3. R. Franzosi, L. Casetti, L. Spinelli, M. Pettini, Phys. Rev. E 60, R5009 (1999)

  4. R. Franzosi, L. Casetti, L. Spinelli, Phys. Rev. Lett. 84, 2774 (2000)

    Google Scholar 

  5. S.A. Safran, P.S. Sahni, G.S. Grest, Phys. Rev. B 28, 2693 (1983)

    Google Scholar 

  6. G.F. Mazenko, O.T. Valls, Phys. Rev. B 27, 6811 (1983)

    Google Scholar 

  7. J. Vinals, M. Grant, M. San Miguel, J.D. Gunton, E.T. Gawlinski, Phys. Rev. Lett. 54, 1264 (1985)

    Google Scholar 

  8. S. Kumar, J. Vinals, J.D. Gunton, Phys. Rev. B 34, 1908 (1986)

    Google Scholar 

  9. A. Lipowski, Physica A 268, 6 (1999)

    Google Scholar 

  10. V. Spirin, P.L. Krapivsky, S. Redner, Phys. Rev. E 65, 016119 (2001)

    Google Scholar 

  11. C. Bäuerie, Yu.M. Bunkov, S.N. Fisher, H. Godfrin, G.R. Pickett, Nature 382, 332 (1995)

    Google Scholar 

  12. S. Digal, R. Ray, A.M. Srivastava, Phys. Rev. Lett. 83, 5030 (1999)

    Google Scholar 

  13. H.R. Trebin, Liq. Cryst. 24, 127 (1998)

    Google Scholar 

  14. W.H. Zurek, Phys. Rep. 276, 177 (1996)

    Google Scholar 

  15. T.W.B. Kibble, J. Phys. A 9, 1387 (1976)

    Google Scholar 

  16. A.J. Bray, Adv. Phys. 43, 357 (1994)

    Google Scholar 

  17. S.M. Allen, J.W. Cahn, Acta Metall. 27, 1085 (1979)

    Google Scholar 

  18. P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)

    Article  Google Scholar 

  19. J.W. Cahn, J.E. Hiliard, J. Chem. Phys. 31, 688 (1959)

    Google Scholar 

  20. N.A. Gross, W. Klein, K. Ludwig, Phys. Rev. E 56, 5160 (1997)

    Google Scholar 

  21. I.M. Lifshitz, Zh. Exp. Teor. Fiz. 42, 1354 (1962)

    Google Scholar 

  22. G. Brown, P.A. Rikvold, M. Sutton, M. Grant, Phys. Rev. E 56, 6601 (1997)

    Google Scholar 

  23. G. Brown, P.A. Rikvold, M. Grant, Phys. Rev. E 58, 5501 (1998)

    Google Scholar 

  24. M. Fialkowski, R. Holyst, Phys. Rev. E 66, 046121 (2002)

    Google Scholar 

  25. G. Brown, P.A. Rikvold, Phys. Rev. E 65, 036137 (2002)

    Google Scholar 

  26. M. Gage, R. Hamilton, J. Diff. Geom. 23, 69 (1986)

    MathSciNet  MATH  Google Scholar 

  27. M. Grayson, J. Diff. Geom. 26, 285 (1987)

    Google Scholar 

  28. G. Huisken, J. Diff. Geom. 20, 237 (1984)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Fiałkowski .

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fiałkowski , M., Hołyst, R. Global symmetry breaking in the nonconserved order parameter system during phase ordering. Eur. Phys. J. E 16, 247–251 (2005). https://doi.org/10.1140/epje/e2005-00025-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epje/e2005-00025-x

PACS.

Navigation