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Recently, a new and efficient algorithm (the LLR method) has been proposedfor computing densities of states in statistical systems and gauge theories. Inthis talk, we explore whether this novel density of states method can beapplied to numerical computations of observables in systems for which theaction is complex. To this purpose, we introduce a generalised density ofstates, in terms of which integrals of oscillating observables can bedetermined semi-analytically, and we define a strategy to compute it with theLLR method. As a case study, we apply these ideas to the Z(3) spin model atfinite density, finding a remarkable agreement of our results for the phasetwist with those obtained with the worm algorithm for all explored chemicalpotentials, including values for which there are cancellations over sixteenorders of magnitude. These findings open new perspectives for dealing with thesign problem on physically more relevant systems.

A novel density of state method for complex action systems