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首页> 外文期刊>Physical review >Thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
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Thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class

机译：卡西米尔热力学力：蒙特卡洛研究普通和正常表面通用性类之间的交叉

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摘要

We study the crossover from the ordinary to the normal surface universality class in the three-dimensional Ising bulk 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_(h1) = 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 i. Finally, we study the approach to the strong adsorption limit h _1→∞. 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 Ising model on the simple cubic lattice [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.
机译：我们研究了三维Ising整体通用性类中从普通表面到普通表面通用性类的转换。这种交叉与在混合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。我们在简单的立方晶格上执行改进的Blume-Capel模型的蒙特卡罗模拟。我们考虑具有薄膜几何形状的系统，其中应用了各种边界条件。我们讨论了由曲面及其与所谓的外推长度的关系引起的缩放比例校正。为此，我们分析了薄膜表面附近的磁化分布行为。对于普通的表面通用性类，我们获得了重归一化组指数y_（h1）= 0.7249（6）的准确估计。接下来，我们研究从普通表面到普通表面通用性类的交叉区域中的卡西米尔热力学力。为此，我们在h_1 = 0处计算跨度有限尺寸缩放函数的泰勒展开式直至h_1中的二阶，其中h_1是其中一个曲面的外部场。我们通过模拟h i的有限值来检查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。我们的结果证实了对二维Ising模型条纹的精确计算得出的定性图像[D. B.亚伯拉罕和A. Maciolek，物理学。牧师105，055701（2010）]，平均场计算和简单立方晶格上的Ising模型的初步蒙特卡洛模拟[T. F.Mohry等人，《物理学报》。 Rev. E 81，061117（2010）]：对于h_1和膜的厚度的某些选择，热力学Casimir力根据温度改变符号，对于温度和h _1的某些选择，它也改变符号是膜厚度的函数。

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