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Inhomogeneous Glauber dynamics and the process of crystallization of a lattice gas

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Abstract

The model under consideration is a hard-core lattice gas in an external potential on a Bethe lattice with nonequilibrium time evolution governed by Glauber dynamics. A hierarchical decoupling of nonequilibrium correlations, motivated by and asymptotically providing the exact form of equilibrium multisite correlations in the inhomogeneous potential regime, is proposed. Application is made to the process of lattice gas crystallization, at high activity, from a spatially homogeneous fluid phase to an equilibrium crystal phase with unequal sublattice densities. The first few levels of the hierarchical decoupling give a consistent picture of two kinds of nonequilibrium instabilities—one leading to a sublattice density bifurcation, the other associated with an abrupt increase in densities and correlations in time.

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References

  1. G. Tarjus, P. Schaaf, and J. Talbot,J. Stat. Phys. 63:167 (1991).

    Google Scholar 

  2. J. A. Given,Phys. Rev. A 45:816 (1992).

    Google Scholar 

  3. J. A. Given and G. R. Stell, Liquid-state theory for irreversible surface adsorption,J. Stat. Phys., to appear.

  4. R. J. Glauber,J. Math. Phys. 4:294 (1963).

    Google Scholar 

  5. J. C. Angles d'Auriac and R. Rammal,J. Phys. A 21:763 (1988).

    Google Scholar 

  6. P. O. Weir and J. M. Kosterlitz,Phys. Rev. B 33:391 (1986).

    Google Scholar 

  7. M. A. Zaluska-Kotur and L. A. Turski,J. Phys. A 22:413 (1989).

    Google Scholar 

  8. T. M. Liggett,Interacting Particle Systems (Springer, Berlin, 1985).

    Google Scholar 

  9. M. Scheucher and H. Spohn,J. Stat. Phys. 53:279 (1988).

    Google Scholar 

  10. M. C. Cross and P. C. Hohenberg,Rev. Mod. Phys. 65:851 (1993).

    Google Scholar 

  11. J. K. Percus,J. Stat. Phys. 16:299 (1977).

    Google Scholar 

  12. L. Šamaj,J. Phys. (Paris)50:273 (1989).

    Google Scholar 

  13. J. K. Percus,J. Stat. Phys. 55:1263 (1989).

    Google Scholar 

  14. A. Robledo and C. Varea,J. Stat. Phys. 63:1163 (1991).

    Google Scholar 

  15. L. K. Runnels,Phys. Rev. Lett. 15:581 (1965).

    Google Scholar 

  16. R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).

    Google Scholar 

  17. R. J. Baxter,J. Phys. A 13:L61 (1980).

    Google Scholar 

  18. B. Widom,J. Stat. Phys. 19:563 (1978).

    Google Scholar 

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Author notes

  1. L. Šamaj

    Present address: Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 842 28, Bratislava, Slovakia

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 10012, New York, New York

    L. Šamaj & J. K. Percus

  2. Physics Department, New York University, 10003, New York, New York

    J. K. Percus

Authors
  1. L. Šamaj
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  2. J. K. Percus
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Šamaj, L., Percus, J.K. Inhomogeneous Glauber dynamics and the process of crystallization of a lattice gas. J Stat Phys 78, 495–512 (1995). https://doi.org/10.1007/BF02183361

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  • DOI: https://doi.org/10.1007/BF02183361

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