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Effects of Field Orientation on the Driven Lattice Gas

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Abstract

Steady states of the driven lattice gas (DLG) on triangular, hexagonal and square lattices with the field at several fixed orientations to the principal lattice vectors were studied by Monte Carlo simulation. In most cases a strong field suppressed change to a low-temperature ordered phase. On each lattice, one field orientation that caused nonequilibrium ordering was identified. On triangular and hexagonal lattices, dependence of energy and anisotropy on field strength was studied at those orientations. Anisotropic ordering along the field developed at intermediate temperatures under weak fields. Partial ordering along the field persisted to low temperature under strong fields.

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References

  1. S. Katz J. L. Lebowitz H. Spohn (1983) ArticleTitlePhase transitions in stationary nonequilibrium states of model lattice systems Phys. Rev. B. 28 IssueID(3 1655–1658 Occurrence Handle10.1103/PhysRevB.28.1655 Occurrence Handle1:CAS:528:DyaL3sXkvFOgurc%3D

    Article  CAS  Google Scholar 

  2. S. Katz J. L. Lebowitz H. Spohn (1984) ArticleTitleNonequilibrium steady states of stochastic lattice gas models of fast ionic conductors J. Stat. Phys. 34 IssueID(3/4 497–537 Occurrence Handle10.1007/BF01018556

    Article  Google Scholar 

  3. B. Schmittmann R. K. P. Zia (1995) Statistical mechanics of driven diffusive systems C. Domb J. L. Lebowitz (Eds) Phase Transitions and Critical Phenomena NumberInSeries17 Academic Press London

    Google Scholar 

  4. J. Marro R. Dickman (1999) Nonequilibrium Phase Transitions in Lattice Models Cambridge University Press Cambridge

    Google Scholar 

  5. R. K. P. Zia B. L. Shaw B. Schmittmann R. J. Astalos (2000) ArticleTitleContrasts between equilibrium and non-equilibrium steady states: Computer aided discoveries in simple lattice gases Comp. Phys.Comm. 127 23–31 Occurrence Handle10.1016/S0010-4655(00)00022-9 Occurrence Handle1:CAS:528:DC%2BD3cXislCgurc%3D

    Article  CAS  Google Scholar 

  6. D. C. Mattis (1985) The Theory of Magnetism II: Thermodynamics and Statistical Mechanics Springer Berlin 100

    Google Scholar 

  7. M. E. J. Newman G. T. Barkema (1999) Monte Carlo Methods in Statistical Physics Clarendon Press Oxford

    Google Scholar 

  8. W. H. Press S. A. Teukolsky W. T. Vetterling B. P. Flannery (1992) Numerical Recipes in C: The Art of Scientific Computing EditionNumber2 Cambridge University Press Cambridge

    Google Scholar 

  9. W. Gropp E. Lusk A. Skjellum (1999) Using MPI: Portable Parallel Programming with the Message-Passing Interface EditionNumber2 MIT Press Cambridge, MA

    Google Scholar 

  10. A. Srinivasan M. D. Ceperley M. Mascagni (1999) Random number generators for parallel applications in Monte Carlo Methods in Chemical Physics D. M. Ferguson J. I. Siepmann D. G. Truhlar (Eds) Advances in Chemical Physics. Series 105 John Wiley and Sons New York 13–36

    Google Scholar 

  11. D. P. Landau K. Binder (2000) A Guide to Monte Carlo Simulations in Statistical Physics Cambridge University Press Cambridge

    Google Scholar 

  12. J. L. Vallés J. Marro (1986) ArticleTitleNonequilibrium phase transitions in stochastic lattice systems: Influence of the hopping rates J. Stat. Phys. 43 IssueID(3/4 441–461 Occurrence Handle10.1007/BF01020647

    Article  Google Scholar 

  13. J. L. Vallés J. Marro (1987) ArticleTitleNonequilibrium second-order phase transitions in stochastic lattice systems: a finite-size scaling analysis in two dimensions J. Stat. Phys. 49 IssueID(1/2 89–119 Occurrence Handle10.1007/BF01009956

    Article  Google Scholar 

  14. R. K. P. Zia L.B. Shaw B. Schmittmann (2000) ArticleTitlePossible existence of an extraordinary phase in the driven lattice gas Physica A. 279 60–68

    Google Scholar 

  15. R. Dickman (1988) ArticleTitleMean-field theory of the driven diffusive lattice gas Phys. Rev. A. 38 2588–2593 Occurrence Handle10.1103/PhysRevA.38.2588 Occurrence Handle9900667

    Article  PubMed  Google Scholar 

  16. Pesheva N. C., A Mean-Field Method For Driven Diffusive Systems Based On Maximum Entropy Principle , Virginia Polytechnic Institute and State University, Ph.D. Thesis, UMI 9000639 (1989).

  17. N. C. Pesheva Y. Shnidman R. K. P. Zia (1993) ArticleTitleA maximum entropy mean field method for driven diffusive systems J. Stat. Phys. 70 IssueID(3/4 737–771 Occurrence Handle10.1007/BF01053593

    Article  Google Scholar 

  18. M. Q. Zhang (1987) ArticleTitleExact results on the steady state of a hopping model Phys. Rev. A. 35 IssueID(5 2266–2275 Occurrence Handle10.1103/PhysRevA.35.2266 Occurrence Handle9898403

    Article  PubMed  Google Scholar 

  19. Zhang Q., Nonequilibrium Steady States of a Stochastic Model System , Rutgers, the State University of New Jersey, Ph.D. Thesis, UMI 8803528 (1987).

  20. K. S. C. Kumaran, Nonequilibrium Steady States of the Lattice Gas, University of Minnesota,. M.S. Thesis (2004).

  21. Wolfram Research Inc, Mathematica, Version 5.0, Champaign, IL (2003).

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Correspondence to Paul D. Siders.

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Siders, P.D. Effects of Field Orientation on the Driven Lattice Gas. J Stat Phys 119, 861–880 (2005). https://doi.org/10.1007/s10955-005-4427-9

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  • DOI: https://doi.org/10.1007/s10955-005-4427-9

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