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Microscopic models of classical degrees of freedom coupled to non-interactingfermions occur in many different contexts. Prominent examples from solid statephysics are descriptions of colossal magnetoresistance manganites and dilutedmagnetic semiconductors, or auxiliary field methods for correlated electronsystems. Monte Carlo simulations are vital for an understanding of suchsystems, but notorious for requiring the solution of the fermion problem witheach change in the classical field configuration. We present an efficient,truncation-free O(N) method on the basis of Chebyshev expanded local Greenfunctions, which allows us to simulate systems of unprecedented size N.

Green-Function-Based Monte Carlo Method for Classical Fields Coupled to Fermions