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Considerable progress has been recently made in the theoretical understandingof the colossal magnetoresistance (CMR) effect in manganites. The analysis ofsimple models with two competing states and a resistor network approximation tocalculate conductances has confirmed that CMR effects can be theoreticallyreproduced using non-uniform clustered states. In this paper, the recentlyproposed Truncated Polynomial Expansion method (TPEM) for spin-fermion systemsis tested using the double-exchange one-band, with finite Hund coupling $J_{\rmH}$, and two-band, with infinite $J_{\rm H}$, models. Two dimensional latticesas large as 48$\times$48 are studied, far larger than those that can be handledwith 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 separatingferromagnetic metallic from insulating states. A huge magnetoresistance isfound at low temperatures by including small magnetic fields, in excellentagreement with experiments. However, at temperatures above the Curie transitionthe effect is much smaller confirming that the standard finite-temperature CMRphenomenon cannot be understood using homogeneous states. By comparing resultsbetween the two methods, TPEM and DIAG, on small lattices, and by analyzing thesystematic behavior with increasing cluster sizes, it is concluded that theTPEM is accurate to handle realistic manganite models on large systems. Ourresults pave the way to a frontal computational attack of the colossalmagnetoresistance phenomenon using double-exchange like models, on largeclusters, and including quenched disorder.Comment: 14 pages, 17 figure

One- and two-band models for colossal magnetoresistive manganites studied using the truncated polynomial expansion method