Higher transcendental functions in statistical theory of strongly anharmonic solids

We report here the solution of a set of transcendental equations that arises in the correlative theory of an unsymmetrized self-consistent field for strongly anharmonic crystals. The solutions of these equations in the case of pairwise forces are higher transcendental functions βn(X), where n is the dimensionality of the lattice and X is a dimensionless combination of temperature and the second-and fourth-order force coefficients. We also solve the corresponding equations for the case of many-body interactions and describe the respective transcendental function v(X, X'). The physical meaning of these functions is that they describe the degree of anharmonicity of the system. The values of these functions can be used as input data for the calculation of the structural, dynamic and thermodynamic properties of solids with strong anharmonicity.