Short-range correlations in modified planar rotator model

TL;DR

This paper introduces a modified planar rotator model inspired by statistical physics that effectively captures short-range spatial correlations in geostatistical data, demonstrated through Monte Carlo simulations and Matérn covariance functions.

Contribution

The paper presents a novel modification of the XY model that models geostatistical spatial correlations using flexible Matérn covariance functions.

Findings

Model captures spatial correlations in geostatistical data.

Correlation range and smoothness vary with temperature and simulation time.

Potential for automatic spatial data prediction in geophysics.

Abstract

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 Mat\'{e}rn 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.