Berezinskii-Kosterlitz-Thouless phase transitions in a kagome spin ice by a quantifying Monte Carlo process: Distribution of Hamming distances
Berezinskii-Kosterlitz-Thouless phase transitions in a kagome spin ice by a quantifying Monte Carlo process: Distribution of Hamming distances
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DOI：
10.1103/physrevb.108.134422
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发表时间：
2023-07
影响因子：
3.7
通讯作者：
Wenjie Su;F. Hu;Chen Cheng;Nvsen Ma
中科院分区：
文献类型：
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作者：
Wenjie Su;F. Hu;Chen Cheng;Nvsen Ma
我们重新研究了具有反铁磁最近邻和铁磁次最近邻相互作用的Kagome晶格上的Ising模型的相变，该模型具有六态时钟自旋冰基态和两个连续的Berezinskiii-Kosterlitz-BKT（BKT）相变。采用经典的蒙特卡罗（MC）模拟，相的特征在于磁序参数，和临界温度得到的相关物理量的有限尺寸标度。此外，我们试图获得一般信息的相变从MC过程中，而不是MC的结果，并成功地提取正确的过渡点，令人惊讶的高精度。具体来说，我们专注于选定的数据集不相关的MC配置和量化的MC过程中使用的分布的两个配置汉明距离在这个小的数据收集。这个分布不仅仅是一个在不同阶段具有不同行为的量，而且还很好地支持与序参量相同的BKT标度形式，从中我们成功地以惊人的高精度确定了两个BKT转变点。我们还讨论了相变和从汉明距离中提取的内在维度之间的联系，汉明距离广泛应用于不断发展的机器学习领域，据报道能够检测临界点。我们的研究结果提供了一个新的理解的自旋冰过渡的Kagome晶格，并有希望被类似地用于确定在同一晶格上的量子系统的过渡与强烈的挫折。
We reinvestigate the phase transitions of the Ising model on the Kagome lattice with antiferromagnetic nearest-neighbor and ferromagnetic next-nearest-neighbor interactions, which has a six-state-clock spin ice ground state and two consecutive Berezinskii-Kosterlitz-Thouless (BKT) phase transitions. Employing the classical Monte Carlo (MC) simulations, the phases are characterized by the magnetic order parameter, and the critical temperatures are obtained by the finite-size scaling of related physical quantities. Moreover, we attempt to gain general information on the phase transitions from the MC process instead of MC results and successfully extract the correct transition points with surprisingly high accuracy. Specifically, we focus on the selected data set of uncorrelated MC configurations and quantify the MC process using the distribution of two-configuration Hamming distances in this small data collection. This distribution is more than a quantity that features different behaviors in different phases but also nicely supports the same BKT scaling form as the order parameter, from which we successfully determine the two BKT transition points with surprisingly high accuracy. We also discuss the connection between the phase transitions and the intrinsic dimension extracted from the Hamming distances, which is widely used in the growing field of machine learning and is reported to be able to detect critical points. Our findings provide a new understanding of the spin ice transitions in the Kagome lattice and can hopefully be used similarly to identify transitions in the quantum system on the same lattice with strong frustrations.