Kinetic lattice gas model of collective diffusion in a one-dimensional system with long-range repulsive interactions

Abstract

Collective diffusion is investigated within the kinetic lattice gas model for systems of particles in one dimension with repulsive long-range interactions which are known to result in a staircaselike phase diagram with an infinite sequence of incompressible crystalline phases separated one from another by unstable compressible liquidlike phases. Using a recently proposed [Gortel and Za\l{}uska-Kotur, Phys. Rev. B 70, 125431 (2004)] variational method, an analytic expression for the particle density dependence of the diffusion coefficient is derived in which commonly postulated static and kinetic factors are unambiguously identified. It is shown that while the static factor exhibits singular coverage dependence due to a sharp drop of compressibility when the system enters a crystalline phase, the kinetic factor may substantially modify this behavior. Depending on details of the activated state interactions controlling the migration kinetics the diffusion coefficient may also be singular or, at another extreme, it may be a continuously smooth function of density. In view of these observations recent results on efficient low temperature self-reorganization through devil's staircase phases in the dense $\mathrm{Pb}∕\mathrm{Si}(111)\text{\ensuremath{-}}\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ are discussed.