  The calculation of two- and four-particle observables is addressed within the
framework of the truncated polynomial expansion method (TPEM). The TPEM
replaces the exact diagonalization of the one-electron sector in models for
fermions coupled to classical fields such as those used in manganites and
diluted magnetic semiconductors. The computational cost of the algorithm is
O(N) -- with N the number of lattice sites -- for the TPEM which should be
contrasted with the computational cost of the diagonalization technique that
scales as O(N^4). By means of the TPEM, the density of states, spectral
function and optical conductivity of a double-exchange model for manganites are
calculated on large lattices and compared to previous results and experimental
measurements. The ferromagnetic metal becomes an insulator by increasing the
direct exchange coupling that competes with the double exchange mechanism. This
metal-insulator transition is investigated in three dimensions.
