The preceding Comment raises a few points concerning our paper [Phys. Rev. E 89, 042116 (2014)]. In this Reply we stress that although Diehl et al. [Europhys. Lett. 100, 10004 (2012) and Phys. Rev. E 89, 062123 (2014)] use three different models to study the Casimir force for the $\mathrm{O}(n\to \infty )$ 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 et al. [Europhys. Lett. 100, 10004 (2012) and Phys. Rev. E 89, 062123 (2014)]. We also present additional evidence supporting our conclusion in Dantchev et al. [Phys. Rev. E 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, whereas $T$ remains well outside of the critical region.

• Received 1 January 2015

DOI:https://doi.org/10.1103/PhysRevE.91.026102