On the accuracy of approximation of the two-particle distribution function for a ferromagnet

When constructing a system of equations of correlation magnetodynamics (a model of a continuous medium of a ferromagnet), the BBGKY hierarchy is used. To close the BBGKY hierarchy, instead of the traditional mean field approximation, an approximation of the two-particle distribution function is used, taking into account correlations between nearest neighbors. One of the goals of this work is to check the quality of this approximation, where «atom-to-atom» modeling using the Landau–Lifshitz equations is taken as a standard. It is shown that the approximation has an average absolute error of the order of 0.001 for the moments of the distribution function. The constructed approximation allows us to obtain the value of the spontaneous magnetization of a separate implementation based on the nonlinearity of the two-particle distribution function for an ensemble of implementations.