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Bulk diffusivity of lattice gases close to criticality

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Abstract

We consider lattice gases where particles jump at random times constrained by hard-core exclusion (simple exclusion process with speed change). The conventional theory of critical slowing down predicts that close to a critical point the bulk diffusivity vanishes as the inverse compressibility. We confirm this claim by proving a strictly positive lower bound for the conductivity.

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References

  1. L. van Hove,Phys. Rev. 93:1374 (1954).

    Google Scholar 

  2. S. Ma,Modern Theory of Critical Phenomena (Benjamin, Reading, Massachusetts, 1976).

    Google Scholar 

  3. P. C. Hohenberg and P. I. Halperin,Rev. Mod. Phys. 49:435 (1977).

    Google Scholar 

  4. P. I. Halperin, P. C. Hohenberg, and S. Ma,Phys. Rev. Lett. 29:1548 (1972).

    Google Scholar 

  5. D. P. Landau, Monte Carlo studies of critical and multicritical phenomena, inApplications of the Monte Carlo Method, K. Binder, ed. (Springer, Berlin, 1984), p. 93.

    Google Scholar 

  6. R. Kutner, K. Binder, and K. W. Kehr,Phys. Rev. B 28:1846 (1983).

    Google Scholar 

  7. T. M. Liggett,The Stochastic Evolution of Infinite Systems of Interacting Particles (Springer, Berlin, 1978).

    Google Scholar 

  8. H.-O. Georgii,Canonical Gibbs Measures (Springer, Berlin, 1979).

    Google Scholar 

  9. I. D. Lawrie and S. Sarbach, Theory of tricritical points, inPhase Transitions and Critical Phenomena, Vol. 9, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1984), p. 1.

    Google Scholar 

  10. R. B. Griffiths,Phys. Rev. B 7:545 (1973).

    Google Scholar 

  11. J. L. Lebowitz, InMathematical Problems in Theoretical Physics, G. Dell' Antonio et al., eds. (Springer, Berlin, 1978), p. 68.

    Google Scholar 

  12. M. Aizenman, Rigorous study of critical behavior, inStatistical Physics and Dynamical Systems, J. Fritz, A. Jaffe, and D. Szász, eds. (Birkhäuser, Boston, 1985).

    Google Scholar 

  13. B. Simon,Statistical Mechanics of Lattice Gases Vol. I (Princeton University Press, Princeton, New Jersey, 1993).

    Google Scholar 

  14. H. Spohn,Large Scale Dynamics of Interacting Particles (Springer, Berlin, 1991).

    Google Scholar 

  15. F. Rezakhanlou,Commun. Math. Phys. 129:445 (1990).

    Google Scholar 

  16. S. R. S. Varadhan, InProceedings Taniguchi Symposium (Kyoto, 1990).

  17. J. Quastel and H. T. Yau, Hydrodynamics of lattice gas with random field at infinite temperature, in preparation.

  18. D. Klein and W. S. Yang, Absence of first order phase transition for antiferromagnetic systems,J. Stat. Phys. 70:1391 (1993).

    Google Scholar 

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Spohn, H., Yau, HT. Bulk diffusivity of lattice gases close to criticality. J Stat Phys 79, 231–241 (1995). https://doi.org/10.1007/BF02179388

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