A method of calculating the free energy and thermodynamic characteristics of the classical n- vector 3D magnetic model at the microscopic level without any adjustable parameters is proposed. The mathematical description is performed using the collective variables method in the framework of the #rho#~4 - model. The exponentially decreasing function of the distance between the particles is used as the interaction potential. Explicit analytical expressions for entropy and specific heat near the phase transition point as functions of the temperature are obtained. The dependence of the critical amplitudes of the thermodynamic characteristics of the system for T>T_c and T展开▼