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Driven nonequilibrium lattice systems with shifted periodic boundary conditions

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Abstract

We present the first study of a driven nonequilibrium lattice system in the two-phase region, withshifted periodic boundary conditions, forcing steps into the interface. When the shift corresponds to small angles with respect to the driving field, we find nonanalytic behavior in the (internal) energy of the system, supporting numerical evidence that interface roughness is suppressed by the field. For larger shifts, the competition between the driving field and the boundary induces the breakup of a single strip with tilted interfaces into many narrower strips with aligned interfaces. The size and temperature dependences of the critical angles of such breakup transitions are studied.

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References

  1. S. Katz, J. L. Lebowitz, and H. Spohn,Phys. Rev. B 28:1655 (1983);J. Stat. Phys. 34:497 (1984).

    Google Scholar 

  2. H. van Beijeren and L. S. Schulman,Phys. Rev. Lett. 53:806 (1984); J. Marro, J. L. Lebowitz, H. Spohn, and M. H. Kalos,J. Stat. Phys. 38:725 (1985); H. van Beijeren, R. Kutner, and H. Spohn,Phys. Rev. Lett. 54:2026 (1985); J. Krug, J. L. Lebowitz, H. Spohn, and M. Q. Zhang,J. Stat. Phys. 44:535 (1986).

    Google Scholar 

  3. K.-t. Leung and J. L. Cardy,J. Stat. Phys. 44:567 (1986); H. K. Janssen and B. Schmittmann,Z. Phys. B 64:503 (1986); K. Gawadzki and A. Kupiainen,Nucl. Phys. B 269:45 (1986).

    Google Scholar 

  4. J. L. Vallés and J. Marro,J. Stat. Phys. 43:441 (1986).

    Google Scholar 

  5. J. L. Vallés and J. Marro,J. Stat. Phys. 49:89 (1987); J. Marro and J. L. Vallés,J. Stat. Phys. 49:121 (1987).

    Google Scholar 

  6. W. K. Burton, N. Cabrera, and F. C. Frank,Phil. Trans. R. Soc. 243:299 (1951); R. L. Dobrushin,Theor. Prob. Appl. (USSR) 17:619 (1972); J. Weeks, G. H. Gilmer, and H. J. Leamy,Phys. Rev. Lett. 31:549 (1973); H. J. Leamy and G. H. Gilmer,J. Cryst. Growth 24/25:499 (1974).

    Google Scholar 

  7. S. T. Chui and J. D. Weeks,Phys. Rev. B 14:4978 (1976); H. van Beijeren,Phys. Rev. Lett. 38:993 (1977); H. J. F. Knops,Phys. Rev. B 20:4670 (1979).

    Google Scholar 

  8. H. van Beijeren and I. Nolden, inTopics in Current Physics, 43, W. Schommers and P. von Blanckenhagen, eds. (Springer, Berlin, 1987), pp. 259–300.

    Google Scholar 

  9. J. W. Cahn,J. Chem. Phys. 66:3667 (1977); C. Ebner and W. F. Saam,Phys. Rev. Lett. 38:1486 (1977).

    Google Scholar 

  10. D. E. Sullivan and M. M. Telo de Gama, Wetting transitions and multilayer adsorption at fluid interfaces, inFluid Interfacial Phenomena, C. A. Croxton, ed. (Wiley, New York, 1985); P. G. de Gennes,Rev. Mod. Phys. 57:827 (1985).

    Google Scholar 

  11. J. S. Langer,Rev. Mod. Phys. 52:1 (1980); J. D. Gunton, M. San Miguel, and P. S. Sahni, inPhase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. Lebowitz, eds. (Academic Press, London, 1983), p. 287.

    Google Scholar 

  12. L. I. Rubinshtefin,The Stefan Problem (American Mathematical Society, Providence, Rhode Island, 1971).

    Google Scholar 

  13. K.-t. Leung,J. Stat. Phys. 50:405 (1988); A. Hernandez-Machado and D. Jasnow,Phys. Rev. A 37:626 (1988).

    Google Scholar 

  14. K.-t. Leung, K. K. Mon, J. L. Vallés, and R. K. P. Zia,Phys. Rev. Lett. 61:1744 (1988), and preprint (1988).

    Google Scholar 

  15. K. K. Mon, S. Wansleben, D. P. Landau, and K. Binder,Phys. Rev. Lett. 60:708 (1988), and preprint (1988).

    Google Scholar 

  16. J. D. Weeks,Phys. Rev. Lett. 52:2160 (1984).

    Google Scholar 

  17. K. Binder, inApplications of Monte Carlo Methods in Statistical Physics, K. Binder, ed. (Springer, Berlin, 1984).

    Google Scholar 

  18. K.-t. Leung, Ph.D. thesis, University of California at Santa Barbara (1987), unpublished.

    Google Scholar 

  19. K.-t. Leung, G. A. Hagedorn and R. K. P. Zia, to be published.

  20. H. van Beijeren, private communication.

  21. L. A. Turski and J. S. Langer,Phys. Rev. A 22:2189 (1977);Acta Metal. 25:1113 (1977); K. Kawasaki and T. Ohta,Physica 118A:175 (1983);Prog. Theor. Phys. 68:129 (1982); D. Jasnow and R. K. P. Zia,Phys. Rev. A 36:2243 (1987); R. K. P. Zia, R. Bausch, H. K. Janssen, and V. Dohm,Mod. Phys. Lett. B 2:961 (1988).

    Google Scholar 

  22. J. Keizer,Statistical Thermodynamics of Nonequilibrium Processes (Springer, New York, 1987).

    Google Scholar 

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Vallés, J.L., Leung, K.t. & Zia, R.K.P. Driven nonequilibrium lattice systems with shifted periodic boundary conditions. J Stat Phys 56, 43–58 (1989). https://doi.org/10.1007/BF01044230

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