English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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 slabwith free boundary conditions, investigated earlier by us [EPL 100, 10004(2012)], is reconsidered using a mean spherical model with separate constraintsfor each layer. The authors (i) question the applicability of theGinzburg-Landau-Wilson approach to the low-temperature regime, arguing for thesuperiority of their model compared to the family of $\phi^4$ models A and Bwhose numerically exact solutions we determined both for values of the couplingconstant $0<g<\infty$ and $g=\infty$. They (ii) report consistency of theirresults with ours in the critical region and a strong manifestation ofuniversality, but (iii) point out discrepancies with our results in the regionbelow $T_{\mathrm{c}}$. We show here that (i) is unjustified and prove that ourmodel B with $g=\infty$ is identical to their spherical model. Hence evidencefor the reported universality is already contained in our work. Moreover, theresults 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 ourresults for the scaling limit. We also show that their low-temperatureexpansion, which does not hold inside the scaling regime, is limited totemperatures lower than they anticipated.

Comment on "Casimir force in the $O(n\to\infty)$ model with free boundary conditions"