  The Green function and the ordering correlation functions of a system of
electrons coupled to acoustic phonons are calculated explicitly. The
sensitivity of the correlation function exponents to the Wentzel-Bardeen
singularity is discussed. A phase diagram is established for the Hubbard model
coupled to phonons, using the integral equations of Lieb and Wu. By increasing
the filling factor towards half filling, the Wentzel-Bardeen singularity can be
reached for arbitrary phonon coupling. This suppresses antiferromagnetic
fluctuations and drives the system in a metallic phase, and ultimately in the
triplet superconducting regime.
