On the Validity of Mode–mode Coupling Theory

We examine the fourth-order mode–mode coupling theory of itinerant magnetism. We explicitly calculate the coupling function, showing that its quantum terms diverge in the limit ωn→0 for wave vectors which are zero or half a reciprocal lattice vector k=12G, if k spans the Fermi surface. The quantum (ωn≠0) terms are often negative and enhance the tendency for magnetic ordering. We show that a self-consistent renormalization of the Gaussian spin susceptibility is not dominated by wave vectors around the magnetic ordering wave vector and by small ωn in d⩾2 dimensions. We propose the use of a local approximation to the mode coupling function, and calculate this function numerically for the tight-binding model and a mean-field theory of the extended t–J model in d=2.