  The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of
classical degrees of freedom coupled to non self-interacting lattices fermions.
The diagonalization of the Hamiltonian matrix is avoided by introducing a
path-integral formulation of the problem, in $d+1$ Euclidean space-time. A
perfect action formulation allows to work on the continuum euclidean time,
without need for a Trotter-Suzuki extrapolation. To demonstrate the feasibility
of the method we study the Double Exchange Model in three dimensions. The
complexity of the algorithm grows only as the system volume, allowing to
simulate in lattices as large as $16^3$ on a personal computer. We conclude
that the second order paramagnetic-ferromagnetic phase transition of Double
Exchange Materials close to half-filling belongs to the Universality Class of
the three-dimensional classical Heisenberg model.
