Comment on "Casimir force in the O(n→∞) model with free boundary conditions"

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
H W DiehlFelix M Schmidt

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 ...Continue Reading

References

May 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel DantchevJoseph Rudnick
Jul 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·H W DiehlFelix M Schmidt

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Citations

Mar 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel DantchevJoseph Rudnick
Jul 16, 2017·Physical Review. E·H W Diehl, Sergei B Rutkevich
Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sergei B Rutkevich, H W Diehl
May 13, 2015·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Francesco Parisen ToldinS Dietrich

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