改进的三维晶格模型的Monte Carlo研究
The thermodynamic Casimir effect in the neighbourhood of the lambda-transition: A Monte Carlo study of an improved three dimensional lattice model
摘要：
本文研究了三维XY普适类薄膜中的热力学Casimir效应。为此，我们在简单立方晶格上模拟了改进的二分量phi^4模型。我们使用的晶格厚度为L_0=33。基于我们的蒙特卡罗模拟的结果，我们计算的通用有限尺寸标度函数θ的热力学Casimir力的行为特征的临界点附近。我们证实了自由边界条件对普遍有限尺寸标度行为的主要修正可以表示为有效厚度L_{0,eff} = L_0+ L_s，其中L_s =1.02（7）.我们的结果进行了比较，与实验的4 He附近的过渡，以前的蒙特卡罗模拟的XY模型的简单立方晶格和场论的结果。对于有限尺寸标度函数θ，我们的结果与~ 4 He薄膜的实验和以前的蒙特卡罗模拟基本一致。
英文摘要：
We study the thermodynamic Casimir effect in thin films in the three dimensional XY universality class. To this end, we simulate the improved two component phi^4 model on the simple cubic lattice. We use lattices up to the thickness L_0=33. Based on the results of our Monte Carlo simulations we compute the universal finite size scaling function theta that characterizes the behaviour of the thermodynamic Casimir force in the neighbourhood of the critical point. We confirm that leading corrections to the universal finite size scaling behaviour due to free boundary conditions can be expressed by an effective thickness L_{0,eff} = L_0+ L_s, with L_s =1.02(7). Our results are compared with experiments on films of 4He near the lambda-transition, previous Monte Carlo simulations of the XY model on the simple cubic lattice and field-theoretic results. Our result for the finite size scaling function theta is essentially consistent with the experiments on films of 4He and the previous Monte Carlo simulations.
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