Calculation of the statistical sum and approximation of multiparticle distribution functions for magnetics in the Heisenberg model

In this paper, we have constructed a direct semi–analytical method for calculating the statistical sum for magnetics in the framework of the Heisenberg model, based on approximation by the exponential of a single integral over the sphere. The calculation results are in good agreement with the atomistic simulation results at least for high temperatures, while the algorithmic complexity of the method is no worse than $O(N^{7/3})$.