使用改进的缩放Ansaetze查找临界点
Finding critical points using improved scaling Ansaetze
摘要：
详细分析了第一次修正的缩放假设，我们开发了加速的方法来确定临界点从有限大小的数据。这些程序的输出是伪临界点的序列，这些伪临界点迅速收敛到真正的临界点。事实上，比以前存在的方法，如现象学重整化群方法更快。我们的方法是有效的，在任何空间维度和量子或经典统计系统。拥有快速收敛的序列，允许在较短的系统尺寸的基础上得出结论，并且在特别困难的情况下，如具有挫折的二维量子系统或发生符号问题时，可能非常重要。我们测试我们的方法的有效性分析的基础上的一维XY模型，并在数值上发生在不可积自旋模型的相变。特别是，我们展示了一种新的均匀性条件方法是如何能够定位的Berezinskiii-Kosterlitz-无边界过渡的发病仅使用基态量相对较小的系统。
英文摘要：
Analyzing in detail the first corrections to the scaling hypothesis, we develop accelerated methods for the determination of critical points from finite size data. The output of these procedures are sequences of pseudo-critical points which rapidly converge towards the true critical points. In fact more rapidly than previously existing methods like the Phenomenological Renormalization Group approach. Our methods are valid in any spatial dimensionality and both for quantum or classical statistical systems. Having at disposal fast converging sequences, allows to draw conclusions on the basis of shorter system sizes, and can be extremely important in particularly hard cases like two-dimensional quantum systems with frustrations or when the sign problem occurs. We test the effectiveness of our methods both analytically on the basis of the one-dimensional XY model, and numerically at phase transitions occurring in non integrable spin models. In particular, we show how a new Homogeneity Condition Method is able to locate the onset of the Berezinskii-Kosterlitz-Thouless transition making only use of ground-state quantities on relatively small systems.
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