Large-n approach to thermodynamic Casimir effects in slabs with free surfaces.
Large-n approach to thermodynamic Casimir effects in slabs with free surfaces.
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具有自由表面的板中热力学卡西米尔效应的大 n 方法
DOI：
10.1103/physreve.89.062123
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Felix M. Schmidt
中科院分区：
文献类型：
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作者：
H. W. Diehl;Daniel Grüneberg;Martin Hasenbusch;Alfred Hucht;Sergei B. Rutkevich;Felix M. Schmidt
具有对称哈密顿量的经典矢量模型在由一对分离的平行自由表面平面界定的板几何中被考虑。包含暗示 Robin 边界条件的标准二次边界项。过量自由能和热力学卡西米尔力的温度相关标度函数在体临界温度、高于和低于体积临界温度的大极限下计算。它们的极限可以用自洽一维薛定谔方程的谱和本征函数来精确表达。该方程通过模型的两个不同离散化版本的数值求解：在第一个模型（“模型 A”）中，仅离散化平板上的坐标，并且对与横向坐标共轭的动量积分进行尺寸正则化；在第二个模型（“模型 B”）中，使用沿横向具有周期性边界条件的简单立方晶格。重整化群的思想被用来表明，除了对标度的修正之外，还应该发生反常的修正。通过对相互作用常数采取适当的 () 限制，可以大大减少它们。根据型号 A 或 B，它们可以在有效厚度内完全或很大程度上被吸收。两种模型都获得了出色的数据崩溃和一致的高精度结果。标度函数的低温戈德斯通值的方法显示涉及对数异常。标度函数表现出在模型的 He 和蒙特卡罗模拟的润湿层变薄实验中看到的所有定性特征，包括下面卡西米尔力的明显最小值。结果符合缩放函数的各种分析已知的精确属性。
The classical-vectormodel withsymmetrical Hamiltonianis considered in aslab geometry bounded by a pair of parallel free surface planes at separation. Standard quadratic boundary terms implying Robin boundary conditions are included in. The temperature-dependent scaling functions of the excess free energy and the thermodynamic Casimir force are computed in the large-limit for temperaturesat, above, and below the bulk critical temperature. Theirlimits can be expressed exactly in terms of the spectrum and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. This equation is solved by numerical means for two distinct discretized versions of the model: in the first (“model A”), only the coordinateacross the slab is discretized and the integrations over momenta conjugate to the lateral coordinates are regularized dimensionally; in the second (“model B”), a simple cubic lattice with periodic boundary conditions along the lateral directions is used. Renormalization-group ideas are invoked to show that, in addition to corrections to scaling, anomalous onesshould occur. They can be considerably decreased by taking an appropriate() limit of theinteraction constant. Depending on the model A or B, they can be absorbed completely or to a large extent in an effective thickness. Excellent data collapses and consistent high-precision results for both models are obtained. The approach to the low-temperature Goldstone values of the scaling functions is shown to involve logarithmic anomalies. The scaling functions exhibit all qualitative features seen in experiments on the thinning of wetting layers ofHe and Monte Carlo simulations ofmodels, including a pronounced minimum of the Casimir force below. The results are in conformity with various analytically known exact properties of the scaling functions.
在大 n 极限下具有自由表面的 O(n) Ï4 模型：边界临界行为、波动引起的力和远壁校正的一些精确结果
DOI：
10.1088/1751-8113/47/14/145004
发表时间：
2014
期刊：
Journal of Physics A: Mathematical and Theoretical
影响因子：
--
作者：
H. W. Diehl;S. B. Rutkevich
通讯作者：
S. B. Rutkevich
O(n) 对称薄膜系统的热力学卡西米尔力的明显最小值：解析理论。
DOI：
10.1103/physreve.90.030101
发表时间：
2014
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
--
作者：
V. Dohm
通讯作者：
V. Dohm