title: Comment on "Casimir force in the O(n→∞) model with free boundary conditions".
abstract: In a recent paper by D. Dantchev, J. Bergknoff, 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 [Europhys. Lett. 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 ϕ(4) models A and B whose numerically exact solutions we determined both for values of the coupling constant 0<g<∞ and for g=∞. 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(c). Here we refute (i) and prove that our model B with g=∞ is identical to their spherical model. Hence evidence for the reported universality is already contained in our paper. 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.
authors.affiliation: Fakultät für Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany.
authors.forename: H W
authors.initials: HW
authors.lastname: Diehl
authors.affiliation: Fakultät für Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany.
authors.forename: Daniel
authors.initials: D
authors.lastname: Grüneberg
authors.affiliation: Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany.
authors.forename: Martin
authors.initials: M
authors.lastname: Hasenbusch
authors.affiliation: Fakultät für Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany.
authors.forename: Alfred
authors.initials: A
authors.lastname: Hucht
authors.affiliation: Fakultät für Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany.
authors.forename: Sergei B
authors.initials: SB
authors.lastname: Rutkevich
authors.affiliation: Fakultät für Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany.
authors.forename: Felix M
authors.initials: FM
authors.lastname: Schmidt