The Kosterlitz–Thouless transition in thin films: a Monte Carlo study of three-dimensional lattice models
The Kosterlitz–Thouless transition in thin films: a Monte Carlo study of three-dimensional lattice models
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薄膜中的 Kosterlitz-Thouless 转变：三维晶格模型的蒙特卡罗研究
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发表时间：
2008
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通讯作者：
M. Hasenbusch
中科院分区：
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作者：
M. Hasenbusch
我们在三维XY普适类中研究薄膜的相变。为此，我们在简单立方晶格上对改进的双组分XY 4模型、改进的动态稀释XY模型和标准XY模型进行了Monte Carlo研究。我们研究膜的厚度高达L0 = 32晶格间距。在晶格的短方向上，采用自由边界条件。使用最近提出的有限尺寸缩放（FSS）方法，我们以高精度确定了转变温度。Binder累积量U4的有效二维有限尺寸标度行为、晶格尺寸上的二阶矩相关长度<$2nd/L、具有反周期和周期边界条件的配分函数之比Za/Zp和螺旋度模量<$p清楚地证实了过渡的无Kosterlitz性质。我们分析了转变温度随薄膜厚度L0的变化规律。我们计算了在三维热力学极限下，在厚度为L0的薄膜的无Kosterlitz-Kosterlitzless转变温度下，薄膜厚度L0与横向相关长度Δ T的普适比：[L0，KT/Δ T]* = 1.595（7）。这一结果可以与4 He薄膜在λ-跃迁附近的实验结果进行比较。
We study the phase transition of thin films in the three-dimensional XY universality class. To this end, we perform a Monte Carlo study of the improved two-component ϕ4 model, the improved dynamically diluted XY model and the standard XY model on the simple cubic lattice. We study films of a thickness up to L0 = 32 lattice spacings. In the short direction of the lattice, free boundary conditions are employed. Using a finite size scaling (FSS) method, proposed recently, we determine the transition temperature with high accuracy. The effectively two-dimensional finite size scaling behaviour of the Binder cumulant U4, the second-moment correlation length over the lattice size ξ2nd/L, the ratio of the partition functions with anti-periodic and periodic boundary conditions Za/Zp and the helicity modulus ϒ clearly confirm the Kosterlitz–Thouless nature of the transition. We analyse the scaling of the transition temperature with the thickness L0 of the film. We compute the universal ratio of the thickness of the film L0 and the transverse correlation length ξT in the three-dimensional thermodynamic limit at the Kosterlitz–Thouless transition temperature of a film of thickness L0: [L0,KT/ξT]* = 1.595(7). This results can be compared with experimental results on thin films of 4He near the λ-transition.