  Thermodynamic properties of the square-lattice Holstein model of the
electron-phonon problem with phonon frequencies small compared to the bare
Fermi energy are obtained using Monte Carlo methods, a strong-coupling
(bipolaronic) expansion, and a weak coupling Migdal-Eliashberg approach.
Already at elevated temperatures where the charge-density wave (CDW) and
superconducting (SC) correlations are very short-range, a crossover occurs as a
function of increasing electron-phonon coupling, $\lambda_0$, from a normal
metallic regime to a pseudogap regime. At sufficiently low $T$, a SC phase is
found for small $\lambda_0$ and a commensurate insulating CDW phase for large
$\lambda_0$.
