摘要翻译：
对于具有O(n)对称哈密顿量的系统，我们将其置于具有宏观横向延伸和有限厚度的D$维平板几何结构中，并在用场论重整化群方法研究了在临界维数$d^*=4$以下的温度涨落在体临界温度$t_{c,\infty}$（热力学Casimir效应）及以上所引起的有效作用力，其中周期和特殊-特殊边界条件对应于两个边界面上表面相互作用的临界增强。如前文[\textit{europhys.lett.}\textbf{75},241(2006)]所示，Landau理论在$t_{c,\infty}$处存在的零模使得传统的RG改进微扰理论在$4-ε$维上定义不清。利用本文提出的修正展开式，计算了过剩自由能和Casimir力对温度$t\geqt_{c,\infty}$的标度函数为$\Mathsf{L}\equivl/\xi\infty$,其中$\xi\infty$为体相关长度。得到了与$L$相关的每面积剩余自由能的标度函数，其$\mathsf{L}\to0$极限与Casimir振幅$\delta_c$到$o(\epsilon^{3/2}）$的结果一致，并显示出更合理的小-$\mathsf{L}$行为，因为它们以$\mathsf{L}\to0$单调逼近临界值$\delta_c$。
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英文标题：
《Thermodynamic Casimir effects involving interacting field theories with
  zero modes》
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作者：
Daniel Gr\"uneberg, H. W. Diehl
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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英文摘要：
  Systems with an O(n) symmetrical Hamiltonian are considered in a $d$-dimensional slab geometry of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$. The effective forces induced by thermal fluctuations at and above the bulk critical temperature $T_{c,\infty}$ (thermodynamic Casimir effect) are investigated below the upper critical dimension $d^*=4$ by means of field-theoretic renormalization group methods for the case of periodic and special-special boundary conditions, where the latter correspond to the critical enhancement of the surface interactions on both boundary planes. As shown previously [\textit{Europhys. Lett.} \textbf{75}, 241 (2006)], the zero modes that are present in Landau theory at $T_{c,\infty}$ make conventional RG-improved perturbation theory in $4-\epsilon$ dimensions ill-defined. The revised expansion introduced there is utilized to compute the scaling functions of the excess free energy and the Casimir force for temperatures $T\geqT_{c,\infty}$ as functions of $\mathsf{L}\equiv L/\xi_\infty$, where $\xi_\infty$ is the bulk correlation length. Scaling functions of the $L$-dependent residual free energy per area are obtained whose $\mathsf{L}\to0$ limits are in conformity with previous results for the Casimir amplitudes $\Delta_C$ to $O(\epsilon^{3/2})$ and display a more reasonable small-$\mathsf{L}$ behavior inasmuch as they approach the critical value $\Delta_C$ monotonically as $\mathsf{L}\to 0$.
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PDF链接：
https://arxiv.org/pdf/710.4436