  An investigation is presented of the utility of semiclassical approximations
for solving the quantum-impurity problems arising in the dynamical-mean-field
approach to the correlated-electron models. The method is based on performing a
exact numerical integral over the zero-Matsubara-frequency component of the
spin part of a continuous Hubbard-Stratonovich field, along with a
spin-field-dependent steepest descents treatment of the charge part. We test
this method by applying it to one or two site approximations to the single band
Hubbard model with different band structures, and comparing the results to
quantum Monte-Carlo and simplified exact diagonalization calculations. The
resulting electron self-energies, densities of states and magnetic transition
temperatures show reasonable agreement with the quantum Monte-Carlo simulation
over wide parameter ranges, suggesting that the semiclassical method is useful
for obtaining a reasonable picture of the physics in situations where other
techniques are too expensive.
