  In a recent paper [D. Dantchev, J. Bergnoff, and J. Rudnick, Phys. Rev. E 89,
042116 (2014)] the problem of the Casimir force in the $O(n)$ model on a slab
with free boundary conditions, investigated earlier by us [EPL 100, 10004
(2012)], is reconsidered using a mean spherical model with separate constraints
for each layer. The authors (i) question the applicability of the
Ginzburg-Landau-Wilson approach to the low-temperature regime, arguing for the
superiority of their model compared to the family of $\phi^4$ models A and B
whose numerically exact solutions we determined both for values of the coupling
constant $0<g<\infty$ and $g=\infty$. They (ii) report consistency of their
results with ours in the critical region and a strong manifestation of
universality, but (iii) point out discrepancies with our results in the region
below $T_{\mathrm{c}}$. We show here that (i) is unjustified and prove that our
model B with $g=\infty$ is identical to their spherical model. Hence evidence
for the reported universality is already contained in our work. Moreover, the
results we determined for anyone of the models A and B for various thicknesses
$L$ are all numerically exact. (iii) is due to their misinterpretation of our
results for the scaling limit. We also show that their low-temperature
expansion, which does not hold inside the scaling regime, is limited to
temperatures lower than they anticipated.
