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]

We present a Density of States calculation with the Functional Fit Approach (DoS FFA) in SU(3) lattice gauge theory with a finite density of static color sources. The DoS FFA uses a parameterized density of states and determines the parameters of the density by fitting data from restricted Monte Carlo simulations with an analytically known function. We discuss the implementation of DoS FFA and the results for a qualitative picture of the phase diagram in a model which is a further step towards implementing DoS FFA in full QCD. We determine the curvature κ in the µ-T phase diagram and find a value close to the results published for full QCD. Introductory remarksThe success of numerical calculations in lattice field theory relies on the availability of probabilistic polynomial algorithms for computing observables in a Monte Carlo (MC) simulation. The key point is the interpretation of the Boltzmann factor e −S as a probability. However, in some situations the action S acquires an imaginary part that spoils the probabilistic interpretation necessary for a MC simulation, a problem usually referred to as "complex action problem" or "sign problem".An important class of systems with a sign problem are lattice field theories with non-zero chemical potential. In many cases the complex action problem is the main obstacle for an ab-initio determination of the full phase diagram at finite density. Different methods such as complex Langevin, Lefshetz thimbles, Taylor expansion, fugacity expansion, reweighting, and worldline formulations were applied to finite density lattice field theory (see, e.g., the reviews [1] -[9] at the annual lattice conferences).Another important general approach are Density of States (DoS) techniques [1], [10] - [27]. Here we develop further the Density of States Functional Fit Approach (DoS FFA) and apply it to SU(3) lattice gauge theory with static color sources (SU (3) LGT-SCS). The DoS FFA was already presented in depth in [24] -[27] and we refer to these papers for a detailed discussion of the method. Here we review only the parts specific for the SU (3) LGT-SCS and the respective observables, which are related to the particle number and its susceptibility used to determine a qualitative picture of the phase diagram.We stress at this point that the results presented here are not meant as a detailed systematic study of the phase diagram of SU (3) LGT-SCS, which would imply a controlled thermodynamical limit followed by extrapolating to vanishing lattice spacing. This paper serves to document the developments and tests of the DoS FFA in a model which is a further step towards a Density of States calculation in full lattice QCD at non-zero chemical potential.

We discuss a variant of density of states (DoS) techniques for lattice field theories, the so-called "functional fit approach" (FFA). The DoS FFA is based on a density of states ρ(x) which is parameterized on small intervals of the argument x of ρ(x). On these intervals restricted Monte Carlo simulations with an additional Boltzmann factor exp(λ x) allow to determine ρ(x) very precisely by obtaining its parameters from fitting the Monte Carlo data to a known function of λ .We describe the method in detail and show its applicability in four different systems, three of which have a complex action problem: The SU(3) spin model with a chemical potential, U(1) lattice gauge theory, the Z 3 spin model with chemical potential, and 2-dimensional U(1) lattice gauge theory with a topological term. In all cases we compare to reference calculations, which partly were done in a dual formulation where the complex action problem is absent. In all four cases we find a very encouraging performance of the DoS FFA.

Abstract. We use the complex φ 4 field at finite density as a model system for developing further techniques based on worldline formulations of lattice field theories. More specifically we: 1) Discuss new variants of the worm algorithm for updating the φ 4 theory and related systems with site weights. 2) Explore the possibility of canonical simulations in the worldline formulation. 3) Study the connection of 2-particle condensation at low temperature to scattering parameters of the theory.

We study the quantum field theory of a charged ϕ^{4} field in lattice regularization at finite density and low temperature in 2 and 4 dimensions with the goal of analyzing the connection of condensation phenomena to scattering data in a nonperturbative way. The sign problem of the theory at nonzero chemical potential μ is overcome by using a worldline representation for the Monte Carlo simulation. At low temperature we study the particle number as a function of μ and observe the steps for 1-, 2-, and 3-particle condensation. We determine the corresponding critical values μ_{n}^{crit}, n=1, 2, 3 and analyze their dependence on the spatial extent L of the lattice. Linear combinations of the μ_{n}^{crit} give the interaction energies in the 2- and 3-particle sectors and their dependence on L is related to scattering data by Lüscher's formula and its generalizations to three particles. For two dimensions we determine the scattering phase shift and for four dimensions the scattering length. We cross-check our results with a determination of the mass and the 2- and 3-particle energies from conventional 2-, 4-, and 6-point correlators at zero chemical potential. The letter demonstrates that the physics of condensation at finite density and low temperature is closely related to scattering data of a quantum field theory.