Developing and testing the density of states FFA method in the SU(3) spin model

Abstract: The Density of States Functional Fit Approach (DoS FFA) is a recently proposed modern density of states technique suitable for calculations in lattice field theories with a complex action problem. In this article we present an exploratory implementation of DoS FFA for the SU(3) spin system at finite chemical potential $\mu$ - an effective theory for the Polyakov loop. This model has a complex action problem similar to the one of QCD but also allows for a dual simulation in terms of worldlines where the complex action problem is solved. Thus we can compare the DoS FFA results to the reference data from the dual simulation and assess the performance of the new approach. We find that the method reproduces the observables from the dual simulation for a large range of $\mu$ values, including also phase transitions, illustrating that DoS FFA is an interesting approach for exploring phase diagrams of lattice field theories with a complex action problem.