Calculation of the partition function of the classical Heisenberg magnet in the linear approximation

The paper presents a new semi-analytical algorithm for calculating the partition function of the classical Heisenberg magnet. The algorithm has similar features to the renormalization group method, widely known in theoretical physics. The similarity of the methods is that the result of single analytical integration is approximated by a function whose form coincides with the original function, which reduces the problem to the previous one. The approximation parameters are calculated either analytically or using the Monte Carlo method. The algorithm developed and implemented in C++ gives correct results at temperatures above the ferromagnet-paramagnet phase transition temperature. Additionally, the developed algorithm enables finding the parameters of many-particle distribution functions, which can be of great importance when constructing models of continuous magnetic media.