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The European Physical Journal Special Topics

, Volume 143, Issue 1, pp 269–272 | Cite as

On the similarities and differences between lattice and off–lattice models of driven fluids

  • M. Díez-Minguito
  • J. Marro
  • P. L. Garrido
Article
  • 74 Downloads

Abstract.

Microscopic modeling of complex systems by cellular automata, which deal with particles at lattice sites interacting via simple local rules, involves some arbitrariness besides a drastic simplification of nature. Here we briefly report on some recent work on the influence of dynamic details on the morphological and critical properties of one of such model systems. In particular, we discuss on the similarities and differences between a kinetic nonequilibrium Ising model—which is a prototype for nonequilibrium anisotropic phase transitions—and its off–lattice counterpart, namely, an analogue in which the spatial coordinates of the particles vary continuously. We also pay attention to a related driven lattice model with nearest-neighbor exclusion.

Keywords

Monte Carlo Monte Carlo Simulation Cellular Automaton European Physical Journal Special Topic Critical Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. B. Chopard, M. Droz, Cellular Automata Modeling of Physical Systems (Cambridge University Press, Cambridge, UK, 1998) Google Scholar
  2. J. Marro, R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, UK, 1999) Google Scholar
  3. S. Katz, J.L. Lebowitz, H. Spohn, Phys. Rev. B 28, 1655 (1983); ibid, J. Stat. Phys. 34, 497 (1984) CrossRefADSGoogle Scholar
  4. B. Schmittmann, R.K.P. Zia, in Statistical Mechanics of Driven Diffusive Systems, in Phase Transitions and Critical Phenomena (Academic, London, UK, 1996) Google Scholar
  5. A. Achahbar, P.L. Garrido, J. Marro, M.A. Muñoz, Phys. Rev. Lett. 87, 195702 (2001) CrossRefADSGoogle Scholar
  6. M. Díez–Minguito, P.L. Garrido, J. Marro, Phys. Rev. E 72, 026103 (2005) CrossRefADSGoogle Scholar
  7. J. Marro, P.L. Garrido, M. Díez–Minguito, Phys. Rev. B 73, 184115 (2006) CrossRefADSGoogle Scholar
  8. M.P. Allen, D.J. Tidlesley, Computer Simulations of Liquids (Oxford University Press, Oxford, UK 1987) Google Scholar
  9. A.D. Rutenberg, C. Yeung, Phys. Rev. E 60, 2710 (1999) CrossRefADSGoogle Scholar
  10. P.I. Hurtado et al., Phys. Rev. B 67, 014206 (2003) CrossRefADSGoogle Scholar
  11. T.M. Squiresa, S.R. Quake, Rev. Mod. Phys. 77, 977 (2005) CrossRefADSGoogle Scholar
  12. M. Díez–Minguito et al. (to be published) Google Scholar
  13. A. Szolnoki, G. Szabó, Phys. Rev. E 65, 047101 (2002) CrossRefADSGoogle Scholar
  14. R. Dickman, Phys. Rev. E 64, 016124 (2001) CrossRefADSGoogle Scholar
  15. K.J. Strandburg, Rev. Mod. Phys. 60, 161 (1988) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • M. Díez-Minguito
    • 1
  • J. Marro
    • 1
  • P. L. Garrido
    • 1
  1. 1.and Departamento de Electromagnetismo y Física de la Materia, Universidad de GranadaInstitute “Carlos I” for Theoretical and Computational PhysicsGranadaSpain

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