A new and efficient method for calculating the total change in the structural energy of a uniform or random system due to a local perturbation is described. The method makes use of an exact algebraic cancellation between terms unchanged by the perturbation and a Green's-function "poles and zeros" method to calculate the changed contributions. The technique is particularly convenient as it uses a continued-fraction formulation which is amenable to well-developed numerical algorithms developed for the recursion programs in Cambridge. The method is applied to two outstanding problems in the theory of magnetism: the excitations in ferromagnetic iron at high temperatures and a direct evaluation of the Heisenberg exchange parameters $J_{\mathrm{ij}}$ out to fifth-nearest neighbor. The calculations support the concept of smoothly varying excitations in iron with a large amount of short-range order above $T_c$. They also indicate that the Heisenberg $J_s$ becomes negative beyond second-nearest neighbor in iron.

• Received 1 August 1980

DOI:https://doi.org/10.1103/PhysRevB.23.3414