title: Coarsening and persistence in a one-dimensional system of orienting arrowheads: Domain-wall kinetics with A+B→0.
abstract: We demonstrate the large-scale effects of the interplay between shape and hard-core interactions in a system with left- and right-pointing arrowheads <> on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain walls, >< (A) and <> (B). The correlation length in the equilibrium state diverges exponentially with increasing arrowhead density, with an ordered state of like orientations arising in the limit. In this high-density limit, the A domain walls diffuse, while the B walls are static. In time, the approach to the ordered state is described by a coarsening process governed by the kinetics of domain-wall annihilation A+B→0, quite different from the A+A→0 kinetics pertinent to the Glauber-Ising model. The survival probability of a finite set of walls is shown to decay exponentially with time, in contrast to the power-law decay known for A+A→0. In the thermodynamic limit with a finite density of walls, coarsening as a function of time t is studied by simulation. While the number of walls falls as t^{-1/2}, the fraction of persistent arrowheads decays as t^{-θ} where θ is close to 1/4, quite different from the Ising value. The global persistence too has θ=1/4, as follows from a heuristic argument. In a generalization where the B walls diffuse slowly, θ varies continuously, increasing with increasing diffusion constant.
authors.affiliation: Department of Applied Physics, Pillai College of Engineering, Sec. 16, New Panvel 410206, India.
authors.forename: Mahendra D
authors.initials: MD
authors.lastname: Khandkar
authors.affiliation: Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom.
authors.forename: Robin
authors.initials: R
authors.lastname: Stinchcombe
authors.affiliation: TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Osman Sagar Road, Hyderabad 500075, India.
authors.forename: Mustansir
authors.initials: M
authors.lastname: Barma