修正的平面旋转体模型中的短程关联
Short-range correlations in modified planar rotator model
摘要：
我们介绍了一个模型的灵感来自统计物理，显示灵活的短程空间相关性，这是潜在的有用的地质统计建模。特别是，我们考虑一个适当修改的平面转子或XY模型，传统上用于建模连续自旋系统的磁性，我们证明，它可以捕捉空间相关性通常存在于地质统计数据。对非平衡态下不同温度和阶段的蒙特卡罗模拟产生的自旋组态的经验研究表明，它们的空间变异性可以用灵活的Matérn协方差函数类来模拟。这些函数的相关范围和平滑度在由温度和模拟时间组成的参数空间中变化显著。我们简要地讨论了该模型的潜力，高效和自动预测的空间数据与短期的相关性，如常见的地球物理和环境应用。
英文摘要：
We introduce a model inspired from statistical physics that is shown to display flexible short-range spatial correlations which are potentially useful in geostatistical modeling. In particular, we consider a suitably modified planar rotator or XY model, traditionally used for modeling continuous spin systems in magnetism, and we demonstrate that it can capture spatial correlations typically present in geostatistical data. The empirical study of the spin configurations produced by Monte Carlo simulations at various temperatures and stages in the nonequilibrium regime shows that their spatial variability can be modeled by the flexible class of Matérn covariance functions. The correlation range and the smoothness of these functions vary significantly in the parameter space that consists of the temperature and the simulation time. We briefly discuss the potential of the model for efficient and automatic prediction of spatial data with short-range correlations, such as commonly encountered in geophysical and environmental applications.
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