  We study the spin and charge fluctuations of the extended Hubbard model (EHM)
with on-site interaction U and first neighbor interaction V on the
two-dimensional square lattice in the weak to intermediate coupling regime. We
propose an extension of the two-particle self-consistent (ETPSC) approximation
that includes the effect of functional derivatives of the pair correlation
functions on irreducible spin and charge vertices. These functional derivatives
were ignored in our previous work. We evaluate them assuming particle-hole
symmetry. The resulting theory satisfies conservations laws and the
Mermin-Wagner theorem. Our current results are in much better agreement with
benchmark Quantum Monte-Carlo (QMC) results. As a function of U and V, we can
determine the crossover temperatures towards renormalized classical regimes
where either spin or charge fluctuations dominate. The dominant wave vector is
self-determined by the approach.
