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首页> 外文期刊>Physical review >Specific heat, internal energy, and thermodynamic Casimir force in the neighborhood of the λ transition
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Specific heat, internal energy, and thermodynamic Casimir force in the neighborhood of the λ transition

机译：比热，内能和λ跃迁附近的卡西米尔热力学力

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摘要

We discuss the relation of the excess specific heat, the excess energy per area, and the thermodynamic Casimir force in thin films. A priori these quantities depend on the reduced temperature t and the thickness L_0 of the film. However finite-size scaling theory predicts that the scaling functions h"(x), h'(x), and θ(x) of these quantities depend only on the combination x=t[L_0/ξ_0]~(1/v), where v is the critical exponent and ξ_0 the amplitude of the correlation length. Furthermore, the finite-size scaling function θ(x) of the thermodynamic Casimir force per area can be expressed in terms of the scaling functions h'(x) and h(x) of the excess energy per area and the excess free energy per area. Here we study this relation at the example of thin films of the improved two-component φ~4 model on the simple cubic lattice. Note that this model undergoes a second-order phase transition that belongs to the three-dimensional XY universality class. First we simulate films with periodic boundary conditions in the short direction and a thickness up to L_0=13 lattice spacings. We find that even for these rather thin films, the predictions of finite-size scaling are well satisfied. We repeat the analysis for films with free boundary conditions. To this end we use Monte Carlo data for the energy per area obtained in previous work. It turns our that corrections to scaling caused by the boundary conditions are very prominent in this case. Only by taking into account these corrections we are able to obtain θ(x) from the excess energy. Finally we repeat this exercise using experimental data for the excess specific heat of ~4He films near the λ transition. The finite-size scaling behavior of the excess specific heat is governed by h"(x), which is proportional to the scaling function f_2 discussed in the literature.
机译：我们讨论了薄膜中过量比热，单位面积过量能量和热力学卡西米尔力的关系。这些量先验地取决于降低的温度t和膜的厚度L_0。但是，有限尺寸缩放理论预测这些量的缩放函数h“（x），h'（x）和θ（x）仅取决于x = t [L_0 /ξ_0]〜（1 / v）的组合，其中v是临界指数，ξ_0是相关长度的幅度，此外，单位面积热力学卡西米尔力的有限尺寸缩放函数θ（x）可以表示为缩放函数h'（x）和单位面积过剩能量和单位面积过剩自由能量的h（x），这里我们以改进的两组分φ〜4模型在简单立方晶格上的薄膜为例研究这种关系。属于三维XY通用性类别的第二阶相变，首先我们模拟在短方向上具有周期性边界条件且厚度最大为L_0 = 13晶格间距的薄膜，即使对于这些相当薄的薄膜，满足了有限尺寸缩放的预测，我们对具有fre的胶片重复分析边界条件。为此，我们将蒙特卡洛数据用于先前工作中获得的每单位面积的能量。这说明我们在这种情况下，由边界条件引起的缩放比例校正非常突出。仅考虑这些校正，我们就能从过剩的能量中获得θ（x）。最后，我们使用实验数据对λ跃迁附近〜4He薄膜的比热过量进行重复此练习。过剩比热的有限尺寸缩放行为由h“（x）控制，它与文献中讨论的缩放函数f_2成比例。

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