论文标题
弥散磁散射的主成分分析：一项理论研究
Principal Component Analysis of Diffuse Magnetic Scattering: a Theoretical Study
论文作者
论文摘要
我们介绍了主成分分析的潜力分析磁性材料中的磁中子散射数据的理论研究。为了解决这个问题，我们为一个模型模拟了散射函数$ s \ left（\ mathbf {q} \ right）$，该模型在不同条件下的不同条件和温度条件下描述具有各向异性旋转旋转相互作用的群集磁体。我们发现较高的维度降低，并且可以通过少数模拟观测值对算法进行训练。随后，可以将观察结果投影到由学习的主组件定义的降低差异空间上。恒定场温度扫描对应于该空间中的轨迹，该轨迹在与地面相对相对应的临界场处显示出特征性分叉。这样的图允许从有限温度测量结果准确确定地面相图。
We present a theoretical study of the potential of Principal Component Analysis to analyse magnetic diffuse neutron scattering data on quantum materials. To address this question, we simulate the scattering function $S\left(\mathbf{q}\right)$ for a model describing a cluster magnet with anisotropic spin-spin interactions under different conditions of applied field and temperature. We find high dimensionality reduction and that the algorithm can be trained with surprisingly small numbers of simulated observations. Subsequently, observations can be projected onto the reduced-dimensionality space defined by the learnt principal components. Constant-field temperature scans corresponds to trajectories in this space which show characteristic bifurcations at the critical fields corresponding to ground-state phase boundaries. Such plots allow the ground-state phase diagram to be accurately determined from finite-temperature measurements.
