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 $A+B\to 0$, quite different from the $A+A\to 0$ 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 $A+A\to 0$. 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 $t^{-\frac{1}{2}}$, the fraction of persistent arrowheads decays as $t^{-\theta }$ where $\theta$ is close to $\frac{1}{4}$, quite different from the Ising value. The global persistence too has $\theta =\frac{1}{4}$, as follows from a heuristic argument. In a generalization where the $B$ walls diffuse slowly, $\theta$ varies continuously, increasing with increasing diffusion constant.

• Received 15 November 2016

DOI:https://doi.org/10.1103/PhysRevE.95.012147