Density of states method for the Z3 spin model

We apply the density of states approach to the Z3 spin model with a chemical potential μ. For determining the density of states we use restricted Monte Carlo simulations on small intervals of the variable for the density. In each interval we probe the response of the system to the variation of a free parameter in the Boltzmann factor. This response is a known function which we fit to the Monte Carlo data and the parameters of the density are obtained from that fit (functional fit approach; FFA). We evaluate observables related to the particle number and the particle number susceptibility, as well as the free energy. We find that for a surprisingly large range of μ the results from the FFA agree very well with the results from a reference simulation in the dual formulation of the Z3 spin model which is free of the complex action problem.