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

Abstract

The proceeding comment raises a few points concerning our paper Dantchev \textit{et al.}, Phys. Rev. E. {\bf 89}, 042116 (2014). In this reply we stress that while Refs. Diehl \textit{et al.} EPL {\bf 100}, 10004 (2012) and Phys. Rev. E. {\bf 89}, 062123 (2014) use three different models to study the the Casimir force for the $O(n\to \infty )$ model with free boundary conditions we study a single model over the entire range of temperatures, from above the bulk critical temperature, $T_c$, to absolute temperatures down to $T=0$. The use of a single model renders more transparent the crossover from effects dominated by critical fluctuations in the vicinity of the bulk transition temperature to effects controlled by Goldstone modes at low temperatures. Contrary to the assertion in the comment, we make no claim for the superiority of our model over any of those considered by Diehl \textit{et al}. We also present additional evidence supporting our conclusion in Dantchev \textit{et al.}, Phys. Rev. E. {\bf 89}, 042116 (2014) that the temperature range in which our low-temperature analytical expansion for the Casimir force increases as $L$ grows and remains accurate for values of the ratio $T/T_c$ that become closer and closer to unity, while $T$ remains well outside of the critical region.

arXiv comment3 pages, 1 table

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• Exact Three Dimensional Casimir Force Amplitude, $C$-function and Binder's Cumulant Ratio: Spherical Model Results
• Large-$n$ approach to thermodynamic Casimir effects in slabs with free surfaces
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• Casimir force in O(n) lattice models with a diffuse interface
• Casimir force in the O(n -> infinity) model with free boundary conditions
• The O(n) ${\varphi }^4$ model with free surfaces in the large-$n$ limit: Some exact results for boundary critical behaviour, fluctuation-induced forces and distant-wall corrections
• Comment on "Casimir force in the $O(n\to \infty )$ model with free boundary conditions"

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• Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface