Short-range correlations in modified planar rotator model

[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 Matern 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.

[发布机构] Institute of Physics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, Koice; 041 54, Slovakia^1;Geostatistics Laboratory, School of Mineral Resources Engineering, Technical University of Crete, Chania; 73100, Greece^2

[效力级别] 数学

[关键词] Automatic prediction;Covariance function;Environmental applications;Geostatistical data;Geostatistical modeling;Nonequilibrium regimes;Short-range correlations;Spatial correlations