Lattice vs. LennardJones models with a net particle flow

1
Lattice vs. Lennard-Jones models with a net
particle flow
Manuel Díez-Minguito, Pedro L. Garrido, and
Joaquín Marro
Institute Carlos I for Theoretical and
Computational Physics, and Departamento de
Electromagnetismo y Física de la Materia
University of Granada, Spain (http//ergodic.ugr
.es)
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Outline

• Objetives (Sims Theory)
• Influence of dynamic details on the resulting
  non-equilibrium steady state (critical
  properties).
• Similarities and differences between a lattice
  model and its continuous (off-lattice)
  counterpart.

• Clue
• Spatial discretization changes morphology and
  induce an spurious phase diagram.

1.- Driven Lattice Gas (DLG) 2.- DLG
robustness 3.- Analog off-lattice model 4.-
Transport and critical behavior 5.- Conclusions
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Driven Lattice Gas (DLG)
N, 2D lattice, PBCs
S.Katz, J. L. Lebowitz, and H. Spohn, J. Stat.
Phys. 34, 497 (1984)
MC simulations (biased Metropolis rule)
(hops against the field forbidden)
particle
hole

• A net current and a straight interface set in.
• 2nd order phase transition

robustness?
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NN
NNN
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Driven Lennard-Jones Fluid (i)
MC sims biased Metropolis rate (Preferential
hopping),

• Condensed and vapor phases segregate
• 2nd order phase transition at (Tc,rc)

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Driven Lennard-Jones Fluid (ii)
Lattice cases enhanced interfacial
conduction. Off-lattice case mostly bulk
conduction.
Critical behavior is consistent with bIsing1/8,
but not with bDLG1/3 or bMF1/2.
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Conclusions

• Our study reveals that spatial discretization
  will often modify the resulting morphological
  properties and even induce different criticality.
• In particular, the critical behavior of the
  driven LJ model is consistent with the Ising one
  (bIsing1/8), but not with its natural lattice
  analog (bDLG1/3).
• This is puzzling in the context of statistical
  field theory given that symmetries seem to bring
  the off-lattice model closer to the driven
  lattice gas than to the equilibrium Ising model.
  The additional freedom of the off-lattice case is
  likely to matter more than suggested by intuition.

(4) Achahbar and MDM (unpublished)
(2) Achahbar et al. PRL 87, 195702 (2001).
(1) F. de los Santos et al. Physica A 296, 364
(2001).
(3) MDM et al. PRE 72, 026103 (2005).