Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany.
Phys Rev E. 2017 Sep;96(3-1):032803. doi: 10.1103/PhysRevE.96.032803. Epub 2017 Sep 25.
We study interfaces with periodic boundary conditions in the low-temperature phase of the improved Blume-Capel model on the simple cubic lattice. The interface free energy is defined by the difference of the free energy of a system with antiperiodic boundary conditions in one of the directions and that of a system with periodic boundary conditions in all directions. It is obtained by integration of differences of the corresponding internal energies over the inverse temperature. These differences can be computed efficiently by using a variance reduced estimator that is based on the exchange cluster algorithm. The interface tension is obtained from the interface free energy by using predictions based on effective interface models. By using our numerical results for the interface tension σ and the correlation length ξ obtained in previous work, we determine the universal amplitude ratios R_{2nd,+}=σ_{0}f_{2nd,+}^{2}=0.3863(6), R_{2nd,-}=σ_{0}f_{2nd,-}^{2}=0.1028(1), and R_{exp,-}=σ_{0}f_{exp,-}^{2}=0.1077(3). Our results are consistent with those obtained previously for the three-dimensional Ising model, confirming the universality hypothesis.
我们研究了改进的 Blume-Capel 模型在简单立方晶格低温相中具有周期性边界条件的界面。界面自由能由沿一个方向具有反周期边界条件的系统的自由能与所有方向具有周期边界条件的系统的自由能之差定义。它通过沿逆温度积分相应的内能差来获得。这些差异可以通过使用基于交换团算法的方差减小估计器来有效地计算。界面张力可以通过使用基于有效界面模型的预测从界面自由能获得。利用我们以前工作中获得的界面张力 σ 和相关长度 ξ 的数值结果，我们确定了普遍的幅度比 R_{2nd,+}=σ_{0}f_{2nd,+}^{2}=0.3863(6), R_{2nd,-}=σ_{0}f_{2nd,-}^{2}=0.1028(1), 和 R_{exp,-}=σ_{0}f_{exp,-}^{2}=0.1077(3)。我们的结果与之前在三维伊辛模型中得到的结果一致，证实了普遍性假设。
