Thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
Thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
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热力学卡西米尔力：普通表面和普通表面普适性类别之间交叉的蒙特卡罗研究
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发表时间：
2010
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通讯作者：
M. Hasenbusch
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作者：
M. Hasenbusch
在三维伊辛普适类中，我们研究了从普通曲面普适类到正常曲面普适类的交叉。这种交叉与离解点附近的二元混合物薄膜的行为以及在一个或两个表面上的弱吸附有关。我们在简立方晶格上对改进的Blume-Capel模型进行了蒙特卡罗模拟。我们考虑具有薄膜几何结构的系统，其中应用了各种边界条件。我们讨论了由曲面引起的标度修正，以及它们与所谓的外推长度的关系。为此，我们分析了薄膜表面附近磁化强度分布的行为。我们得到了一般表面普适性类的重整化群指数y_{h_1}=0.7249(6)的精确估计。接下来，我们研究了从普通表面普适性类到正常表面普适性类交叉区的热力学Casimir力。为此，我们计算了在h_1=0附近的二阶交叉有限尺度函数的Taylor展开，其中h_1是其中一个曲面上的外场。通过对h_1有限值的模拟，检验了泰勒展开式的适用范围。最后，我们研究了强吸附极限h_1的方法。我们的结果证实了从二维伊辛模型条纹的精确计算中出现的定性图景[D.B.Abraham和A.Maciolek，Phys.莱特牧师。105,055701(2010年)]，平均场计算和3DIsing模型的初步蒙特卡罗模拟，[T.F.Mohry等，Phys.Rev.E81,061117(2010年)]：对于某些选择的h_1和薄膜厚度，热力学Casimir力作为温度的函数改变符号，而对于某些选择的温度和h_1，它也作为薄膜厚度的函数改变符号。
We study the crossover from the ordinary to the normal surface universality class in the three-dimensional Ising universality class. This crossover is relevant for the behavior of films of binary mixtures near the demixing point and a weak adsorption at one or both surfaces. We perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. We consider systems with film geometry, where various boundary conditions are applied. We discuss corrections to scaling that are caused by the surfaces and their relation with the so called extrapolation length. To this end we analyze the behavior of the magnetization profile near the surfaces of films. We obtain an accurate estimate of the renormalization group exponent y_{h_1}=0.7249(6) for the ordinary surface universality class. Next we study the thermodynamic Casimir force in the crossover region from the ordinary to the normal surface universality class. To this end, we compute the Taylor-expansion of the crossover finite size scaling function up to the second order in h_1 around h_1=0, where h_1 is the external field at one of the surfaces. We check the range of applicability of the Taylor-expansion by simulating at finite values of h_1. Finally we study the approach to the strong adsorption limit h_1 \rightarrow \infty. Our results confirm the qualitative picture that emerges from exact calculations for stripes of the two-dimensional Ising model, [D. B. Abraham and A. Maciolek, Phys. Rev. Lett. 105, 055701 (2010)], mean-field calculations and preliminary Monte Carlo simulations of the 3D Ising model, [T. F. Mohry et al, Phys. Rev. E 81, 061117 (2010)]: For certain choices of h_1 and the thickness of the film, the thermodynamic Casimir force changes sign as a function of the temperature and for certain choices of the temperature and h_1, it also changes sign as a function of the thickness of the film.