A Mean Field Theory for Biased Lattice Gas Models

  • H. J. Bussemaker
  • M. H. Ernst
Part of the NATO ASI Series book series (NSSB, volume 292)


In this paper we discuss the consequences of biased transition probabilities in a 7-bits FHP lattice gas model on a triangular lattice [1]. A mean field theory is presented that for physically acceptable choices of the transition matrix gives an excellent prediction of the average occupation numbers. We introduce a factorizability condition, the violation of which gives rise to correlations that are reasonably well predicted by the mean field theory. A more detailed treatment of the subject can be found in [2] and [3].


Triangular Lattice Propagation Step Average Occupation Excellent Prediction Factorize Equilibrium 
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  1. [1]
    D. d’Humières and P. Lallemand, Complex Systems 1, 599 (1987)MathSciNetGoogle Scholar
  2. [2]
    H.J. Bussemaker and M.H. Ernst, in proceedings of NATO Advanced Research Workshop on Lattice Gas Automata: Theory, Implementation and Simulation, held in Nice, June 25-28 1991 (to be published in J. Stai. Phys.)Google Scholar
  3. [3]
    H.J. Bussemaker and M.H. Ernst, to be publishedGoogle Scholar
  4. [4]
    U. Frisch, D. d’Humières, B. Hasslacher, P. Lallemand, Y. Pomeau and J.-P. Rivet, Complex Systems 1, 649 (1987) [reprinted in Lattice gas methods for partial differential equations, G. Doolen ed. (Addison-Wesley, Singapore, 1990)]MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • H. J. Bussemaker
    • 1
  • M. H. Ernst
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of UtrechtUtrechtThe Netherlands

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