Green's Functions of the Face-Centered-Cubic Heisenberg Ferromagnet with Second-Neighbor Interactions

Abstract

Green's functions for a fcc Heisenberg ferromagnet with both first- and second-neighbor interactions are given in terms of accurate but simple polynomial approximants. These polynomial approximations greatly simplify the application of sophisticated theory to real physical systems of interest. Our procedure for the calculation of the lattice Green's functions is described. We have computed 24 Green's functions (corresponding to 24 values of the lattice vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}}$), each for a range of values of the first- and second-neighbor exchange constants (${J}_{1}>0, 0>{J}_{2}>\ensuremath{-}{J}_{1}$), and each as a function of energy within the spin-wave band. This enormous quantity of data is condensed by fitting the functions to polynomials in the energy variable, and we tabulate the coefficients of these polynomials. The polynomials not only provide compact representations of the Green's functions (without which Green's-functions theories are useless for applications), but they provide representations which permit Green's-functions theories often to be evaluated analytically. As the polynomials have been formulated to have the rigorously correct analytic behavior at band edges and at Van Hove singularities, results obtained by use of our polynomial approximants are similarly rigorous at the crucial regions of the spectrum, and are highly accurate (\ensuremath{\sim}0.2%) everywhere.