THE RANDOM-PHASE-APPROXIMATION IN THE WEAK-COUPLING REGIME OF THE SQUARE LATTICE HALF-FILLED HUBBARD-MODEL

We re-examine the random-phase approximation (RPA) in the antiferromagnetic spin-density-wave state of the half-filled square lattice repulsive Hubbard model. It is shown that for U/t much less than 1 the RPA yields a vanishing spin-wave velocity, HBARc is similar to 2pi-1/2t(U/t)1/4, a diverging uniform transverse susceptibility, chi(perpendicular-to is similar to (2pit)-1 (U/t)-1/2, and a constant spin stiffness, rho(s) is similar to 2pi-2 t. The behavior of rho(s) shows that the RPA cannot be correct in the weak coupling regime, because rho(s) should vanish in the limit U/t-->0. We give a formally exact expression for rho(s) and identify the term which is neglected within the RPA.