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

TL;DR

This paper introduces the functional fit approach (FFA), a density of states technique for lattice field theories that accurately determines the density of states using restricted Monte Carlo simulations, effectively addressing complex action problems.

Contribution

The paper presents the FFA method, a novel density of states technique that parameterizes rho(x) on small intervals and fits Monte Carlo data to known functions for precise results.

Findings

FFA performs well on systems with complex action problems.

The method yields results consistent with dual formulations.

FFA demonstrates high accuracy across multiple lattice models.

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 rho(x) which is parameterized on small intervals of the argument x of rho(x). On these intervals restricted Monte Carlo simulations with an additional Boltzmann factor exp(lambda x) allow to determine rho(x) very precisely by obtaining its parameters from fitting the Monte Carlo data to a known function of lambda. 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.