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arXiv 1502.07408cond-mat.stat-mech
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对“自由边界条件下$O(n\to\infty)$模型中的Casimir力”一文的答复

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

Daniel Dantchev, Jonathan Bergknoff, Joseph Rudnick

备注：
3 pages, 1 table
发表信息：
Phys. Rev. E 91, 026102 (2015)
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摘要：

接下来的评论提出了几点关于我们的论文Dantchev \textit{et al.}，物理学修订版E。{ \bf 89}，042116（2014）。在这个答复中，我们强调，虽然参考。Diehl \textit{et al.} EPL { \bf 100}，10004（2012）和Phys.Rev.E. { \bf 89}，062123（2014）使用三种不同的模型来研究具有自由边界条件的$O(n \rightarrow \infty)$模型的Casimir力，我们在整个温度范围内研究单个模型，从高于体临界温度$T_c$到绝对温度下至$T=0$。使用一个单一的模型呈现出更透明的交叉，从主要由临界波动在附近的散装转变温度的戈德斯通模式在低温下控制的效果。与评论中的断言相反，我们没有声称我们的模型优于Diehl \textit{et al}所考虑的任何模型。我们还提供了支持我们在Dantchev \textit{et al.}，Phys. Rev. E中的结论的额外证据。{ \bf 89}，042116（2014），我们的卡西米尔力的低温分析展开的温度范围随着$L$的增长而增加，并且对于越来越接近于1的比率$T/T_c$的值保持准确，而$T$保持在临界区域之外。

英文摘要：

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 $O(n \rightarrow \infty)$ 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.

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