Jamming by shape in kinetically constrained models

We derive expressions for the critical density for jamming in a hyper-rhomboid system of arbitrary shape in any dimension for the Kob-Andersen and Fredrickson-Andersen kinetically constrained models. We find that changing the system's shape without altering its total volume or particle density may induce jamming. We also find a transition between shapes in which the correlation length between jammed particles is infinite and shapes that have a finite correlation length.