  Considerable progress has been recently made in the theoretical understanding
of the colossal magnetoresistance (CMR) effect in manganites. The analysis of
simple models with two competing states and a resistor network approximation to
calculate conductances has confirmed that CMR effects can be theoretically
reproduced using non-uniform clustered states. In this paper, the recently
proposed Truncated Polynomial Expansion method (TPEM) for spin-fermion systems
is tested using the double-exchange one-band, with finite Hund coupling $J_{\rm
H}$, and two-band, with infinite $J_{\rm H}$, models. Two dimensional lattices
as large as 48$\times$48 are studied, far larger than those that can be handled
with standard exact diagonalization (DIAG) techniques for the fermionic sector.
The clean limit (i.e. without quenched disorder) is here analyzed in detail.
Phase diagrams are obtained, showing first-order transitions separating
ferromagnetic metallic from insulating states. A huge magnetoresistance is
found at low temperatures by including small magnetic fields, in excellent
agreement with experiments. However, at temperatures above the Curie transition
the effect is much smaller confirming that the standard finite-temperature CMR
phenomenon cannot be understood using homogeneous states. By comparing results
between the two methods, TPEM and DIAG, on small lattices, and by analyzing the
systematic behavior with increasing cluster sizes, it is concluded that the
TPEM is accurate to handle realistic manganite models on large systems. Our
results pave the way to a frontal computational attack of the colossal
magnetoresistance phenomenon using double-exchange like models, on large
clusters, and including quenched disorder.
