  For systems with infinite-order phase transitions, in which an order
parameter smoothly becomes nonzero, a new observable for finite-size scaling
analysis is suggested. By construction this new observable has the favourable
property of diverging at the critical point. Focussing on the example of the
F-model we compare the analysis of this observable with that of another
observable, which is also derived from the order parameter but does not
diverge, as well as that of the associated susceptibility. We discuss the
difficulties that arise in the finite-size scaling analysis of such systems. In
particular we show that one may reach incorrect conclusions from large-system
size extrapolations of observables that are not known to diverge at the
critical point. Our work suggests that one should base finite-size scaling
analyses for infinite-order phase transitions only on observables that are
guaranteed to diverge.
