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 µ -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 µ 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.arXiv:1607.07340v2 [hep-lat]

Functional Fit Approach (FFA) for Density of States method: SU(3) spin system and SU(3) gauge theory with static quarks

“…We observe good agreement between the two different methods up to µ ≈ 4 for n and up to µ ≈ 2 for χ n . This confirms the reliability of the DoS FFA for n and χ n in the respective ranges of µ( see [9] for a more detailed discussion). SU (3) LGT-SCS, up to today, has no dual formulation.…”

“…Both can be motivated from QCD and inherit the complex action problem from QCD. Results for the SU(3) spin model were already discussed in [9], such that here the discussion of that case is kept short.…”

“…New methods based on parameterizing the density on small intervals and computing the parameters with restricted Monte Carlo simulations might be able to overcome the precision problem and could make DoS techniques a reliable tool for finite density calculations. Among these modern DoS techniques are the LLR approach [2,3,4,5,6] and the Functional Fit Approach (FFA), which we use here [7,8,9,10]. For an overview of more conventional DoS strategies see, e.g., the references in the reviews [1,13].…”

Density of states

“…For an alternative method to calculate the coefficients a(E), we point the reader to the Functional Fit Approach [14,15].…”

“…Other methods such as the Functional Fit Approach [14,15] have been proposed to extract the slope a(E) although more work to establish a systematic error control might be needed.…”