ON THE VALIDITY OF MODE-MODE COUPLING THEORY

We examine the fourth-order mode-mode coupling theory of itinerant mag netism. We explicitly calculate the coupling function, showing that it s quantum terms diverge in the limit omega(n) --> 0 for wave vectors w hich are zero or half a reciprocal lattice vector k = 1/2 G. if k span s the Fermi surface. The quantum (omega(n) not equal 0) terms are ofte n negative and enhance the tendency for magnetic ordering. We show tha t a self-consistent renormalization of the Gaussian spill susceptibili ty is not dominated by wave vectors around the magnetic ordering wave vector and by small omega(n) in d greater than or equal to 2 dimension s. We propose the use of a local approximation to the mode coupling fu nction, and calculate this function numerically for the tight-binding model and a mean-field theory of the extended t-J model in d = 2. (C) 1998 Elsevier Science B.V. All rights reserved.