Studies of driven diffusive systems


Driven diffusive systems have been studied extensively in the past decade for their unorthodox nonequilibrium properties[1]. We have studied in particular the finite-size effects and the derivation of suitable continuum theories.

Since the validity of the standard field theory of driven diffusive system has been questioned[2], we decided to do a stringent test of the field theory
by conducting a precise anisotropic finite-size scaling analysis of the 3-dimensional driven diffusive lattice gas[3]. Using a fast multispin coding technique, statistics several orders of magnitude better than before were obtained. Our results strongly support the field-theoretical prediction[4] and rule out the competing proposal[2], hence resolving a long-standing controversy concerning the universality class of critical exponents.

Another attempt to settle the controversy is a proposal of an approximate scheme to derive the continuum Langevin equation from discrete microscopics for stochastic systems[5]. The method was tested with the Ising model and driven diffusive systems. The results derived are in complete agreement with known approaches. Apart from reassuring our previous belief[4] in the
standard field theory of driven diffusive system, the method is generally useful when more systematic and rigorous approaches fail, and when microscopic inputs in the continuum theory are desired.

For the generalization of the driven diffusive system to two species motivated by ionic conductors and traffic flow, we developed a continuum theory and compared to simulations[6]. Excellent agreements were found. We discovered an intriguing transport property in which the cluster of particles drifts backwards with respect to the majority, contrary to naive expectation. It was explained by means of the asymmetry in the particle/hole mobility inside the cluster.


  1. Statistical mechanics of driven diffusive systems,
    B. Schmittmann and R.K.P. Zia, in: Phase Transitions and Critical Phenomena
    Vol. 17, eds. C. Domb and J.L. Lebowitz, (Academic Press, N.Y., 1995).
  2. F. de los Santos and P.L. Garrido, Phys. Rev. E 61, R4683 (2000), and references therein.
  3. Anisotropic Finite-size scaling analysis of a three-dimensional driven diffusive system,
    K.-t. Leung and J.S. Wang, Int. J. Mod. Phys. C 10, 853 (1999).
    Also e-print cond-mat/9805285.
  4. Viability of competing field theories for the driven lattice gas,
    B. Schmittmann, H.K. Janssen, U.C. Tauber, R.K.P. Zia, K.-t. Leung, J.L. Cardy,
    Phys. Rev. E 61, 5977 (2000). Also e-print cond-mat/9912286.
  5. Heuristic derivation of continuum kinetic equations from microscopic dynamics,
    K.-t. Leung, Phys. Rev. E 63, 016102 (2001). Also e-print cond-mat/0006217.
  6. Drifting spatial structures in a system with Oppositely driven species,
    K.-t. Leung and R.K.P. Zia, Phys. Rev. E 56, 308 (1997).

Last revised October 7, 2002 ©KtL