Density of states techniques for lattice field theories using the functional fit approach (FFA)

Abstract

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.

Computing the density of states with the global Hybrid Monte Carlo

“…At action value s, the density of states ρ(s) is defined via the functional integral [3] for the case of a generic observable). The LLR algorithm is a numerical method to compute the density of states from first principles that has proved to be very efficient in different models [3,4,5,6] (see also the contributions [7,8,9,10] to this conference). However, it relies on a simulation of the system in action intervals of given amplitude δ S .…”