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An anisotropic cubic ferromagnetic is investigated using the theory proposed by the present author in earlier papers. The cases of pseudodipolar coupling and of spin quantum number S = 1/2 are considered. The free energy of a ferromagnetic is derived in the form of an infinite convergent series of connected ladder diagrams. The accuracy of this method is restricted to terms proportional to the power 3/2 of the quotient of the absolute and Curie temperatures and to the square of the pseudodipolar coupling constant. Kinematic interaction is shown to be negligible to the accuracy adopted.

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A modification of Dyson's theory of a cubic ferromagnetic is proposed, based on a consideration of the smallness of the kinematical interaction of spin waves at low temperatures and leading to the introduction of Bloch's statistical function with Dyson's Hamiltonian or, equivalently, of the grand partition function. This approach makes possible the use of thermodynamical perturbation calculus according to Matsubara, whose formalism yields the logarithm of the grand partition function as the sum of Bloch's term and distinct parts of the connected ladder diagrams (Dyson's term). In the long spin-wave approximation (at low temperatures), Bloch's term yields a contribution to the magnetization in the form of a series of 3/2, 5/2, and 7/2 powers of the Kelvin/Curie temperature ratio. Dynamical interaction of the spin waves contributes to the magnetization at least as T A by means of the connected diagrams of all order. All coefficients in the magnetization series obtained are identical with the corresponding quantities in Dyson's theory.