螺旋周期边界条件下Compass模型中的方向有序转变的再检验
Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions
摘要：
利用蒙特卡罗模拟研究了二维正方晶格上经典和量子罗盘模型中的方向有序跃迁。提出了一种改进的算法，该算法建立在Wolff聚类算法的一维子空间的配置空间。这种改进使我们能够研究经典系统的$L=512$。基于新的算法，我们给出了证据的存在强烈的反常标度的周期性边界条件，这是比以前预期的更糟糕。我们提出并研究了替代边界条件的指南针模型，不利用扩展的配置空间，并表明他们完全消除了问题与有限尺寸标度。在最后一部分中，我们将这些边界条件应用到量子问题中，并提出了一个相当改进的临界温度的估计，这应该是未来研究的指南针模型的兴趣。我们的调查确定了一个强大的一维磁有序的趋势与一个大的相关长度的不寻常的缩放的原因，而且允许一个精确的量化所涉及的异常长度尺度。
英文摘要：
We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster algorithm in one-dimensional subspaces of the configuration space. This improvement allows us to study classical systems up to $L=512$. Based on the new algorithm we give evidence for the presence of strongly anomalous scaling for periodic boundary conditions which is much worse than anticipated before. We propose and study alternative boundary conditions for the compass model which do not make use of extended configuration spaces and show that they completely remove the problem with finite-size scaling. In the last part, we apply these boundary conditions to the quantum problem and present a considerably improved estimate for the critical temperature which should be of interest for future studies on the compass model. Our investigation identifies a strong one-dimensional magnetic ordering tendency with a large correlation length as the cause of the unusual scaling and moreover allows for a precise quantification of the anomalous length scale involved.
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