Density of states method for the Z(3) spin model

TL;DR

This paper employs the density of states method with a functional fit approach to study the Z(3) spin model at finite chemical potential, successfully overcoming the complex action problem and validating results against dual formulation simulations.

Contribution

It introduces a functional fit approach to determine the density of states in the Z(3) spin model with chemical potential, enabling accurate calculations over a wide parameter range.

Findings

FFA results agree with dual formulation simulations

Effective in a large range of chemical potential values

Accurately computes particle number and susceptibility

Abstract

We apply the density of states approach to the Z(3) spin model with a chemical potential mu. For determining the density of states we use restricted Monte Carlo simulations on small intervals of the variable for the density. In each interval we probe the response of the system to the variation of a free parameter in the Boltzmann factor. This response is a known function which we fit to the Monte Carlo data and the parameters of the density are obtained from that fit (functional fit approch; FFA). We evaluate observables related to the particle number and the particle number susceptibility, as well as the free energy. We find that for a surprisingly large range of mu the results from the FFA agree very well with the results from a reference simulation in the dual formulation of the Z(3) spin model which is free of the complex action problem.