Journal of Statistical Physics

, Volume 34, Issue 3–4, pp 497–537 | Cite as

Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors

  • Sheldon Katz
  • Joel L. Lebowitz
  • Herbert Spohn


We investigate theoretically and via computer simulation the stationary nonequilibrium states of a stochastic lattice gas under the influence of a uniform external fieldE. The effect of the field is to bias jumps in the field direction and thus produce a current carrying steady state. Simulations on a periodic 30 × 30 square lattice with attractive nearest-neighbor interactions suggest a nonequilibrium phase transition from a disordered phase to an ordered one, similar to the para-to-ferromagnetic transition in equilibriumE=0. At low temperatures and largeE the system segregates into two phases with an interface oriented parallel to the field. The critical temperature is larger than the equilibrium Onsager value atE=0 and increases with the field. For repulsive interactions the usual equilibrium phase transition (ordering on sublattices) is suppressed. We report on conductivity, bulk diffusivity, structure function, etc. in the steady state over a wide range of temperature and electric field. We also present rigorous proofs of the Kubo formula for bulk diffusivity and electrical conductivity and show the positivity of the entropy production for a general class of stochastic lattice gases in a uniform electric field.

Key words

Steady states stochastic lattice gas models fast ionic conductors 


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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • Sheldon Katz
    • 1
  • Joel L. Lebowitz
    • 1
  • Herbert Spohn
    • 1
  1. 1.Department of Mathematics and PhysicsRutgers UniversityNew Brunswick

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