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Non-equilibrium Phase Transitions and Steady States in Biased Diffusion of Two Species


Gyorgy Korniss

PhD Dissertation submitted to the Faculty of the Virginia Tech in partial fulfillment of the requirements for the degree of

Doctor of Philosophy




Beate Schmittmann, Chair
James R. Heflin
Guy J. Indebetouw
Clayton D. Williams
Royce K. P. Zia

April 21, 1997
Blacksburg, Virginia


We investigate the dynamics of a three-state stochastic lattice gas, consisting of holes and two oppositely "charged" species of particles, under the influence of an "electric" field, at zero total charge. Interacting only through an excluded volume constraint, particles can hop to nearest neighbor empty sites, but particle-particle exchange between oppositely charged particles is also allowed on a separate time scale. Controlled by this relative time scale, particle density and drive, the system orders into a charge-segregated state. Using a combination of Monte Carlo simulations and continuum field theory techniques, we study the order of these transitions and map out the steady state phase diagram of the system. On a single sheet of transitions, a line of multicritical points is found, separating the first order and continuous transitions. Furthermore, we study the steady-state structure factors in the disordered phase where homogeneous configurations are stable against small harmonic perturbations. The average structure factors show a discontinuity singularity at the origin which in real space predicts an intricate crossover between power laws of different kinds. We also seek for generic statistical properties of these quantities. The probability distributions of the structure factors are universal asymmetric exponential distributions.

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