Comment on "Casimir force in the O(n→∞) model with free boundary conditions" - Diehl, Hans-Werner; Grüneberg, Daniel; Hasenbusch, Martin; Hucht, Alfred; Rutkevich, Sergei B.; Schmidt, Felix M. (Physical review. E, Statistical, nonlinear, and soft matter physics, 2015)
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 ϕ4 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 Tc. 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.
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