A diagrammatic expanding or the density correlation function

The Behaviour of Thermodynamic Quantities Close to the Critical Point. The Itinerant Ferromagnet

“…We begin by considering the Ssing function, it being the simpler of the two. Anticipating the result A91, which we shall later show to be true, we can neglect all terms of order lower than Aka, Ap2 and Aqa in the energy denominators of (3)(4)(5)(6)(7)(8)(9)(10)(11). The neglected terms do not contribute to the dominant part of the integral.…”

“…To start with a relatively simple example, let us consider those elementary collective excitations which are describable by quasiparticle modes. The excitation energy corresponding to the mode of momentum k is given by R(k), where si) is made independent of energy by a suitable choice of the dimensionality factor q(k, E ) (see [9]). But unlike in other expansion schemes, the complicated energy dependence of the correlation function is not discarded but incorporated into S(k, E ) which always is energy dependent.…”

“…Following an argument due to Sherrington [8], it can be shown that, [9], the f-sum rule obeyed by the spin and density correlation function takes the form…”

“…Therefore we use another approach in which these requirements are fulfilled in a more direct way. This is the functional integral formulation of the density field method due to Sherrington [8] and its extension to general order by Bhagavan and Lambert [9].…”

“…The formalism and the notation are as in [9]. a and y denote the z-component of the electron spin with the values ++.…”