  We investigate the response of an electron system which exhibits ideal
nesting features. Using the standard Matsubara formalism we derive analytic
expressions for the imaginary and real parts of the bare particle-hole
susceptibility. The imaginary part has sharp peaks whose maxima at the nesting
momenta approximately scale with frequency divided by temperature. The peak
lineshapes resemble neutron scattering data on chromium and some copper oxide
superconductors. The real part of the bare susceptibility at the nesting
vectors diverges logarithmically at low temperatures. Analytic formulas for the
first vertex correction to the susceptibility are derived for a Hubbard
interaction, and its momentum and temperature variations are calculated
numerically. This term detracts substantially from the ordinary RPA terms for
intermediate values of the Coulomb repulsion. Exact cancellation of a certain
class of diagrams at half filling is shown to result from particle-hole
symmetry. We discuss the consequences of these results for spin fluctuation
theories of high temperature superconductors and spin density wave
instabilities.

Strongly Correlated Electrons;Superconductivity