The Z3 model with the density of states method

TL;DR

This paper introduces a new density of states method applied to the Z3 spin model at finite density, utilizing Monte Carlo simulations to accurately determine the density of states with reduced statistical errors.

Contribution

The paper presents a novel variant of the density of states method that uses one-parameter fits to Monte Carlo data, improving accuracy and efficiency in studying the Z3 spin model.

Findings

Good agreement with dual representation results

Reduced statistical errors compared to other methods

Effective determination of density of states across parameters

Abstract

In this contribution we apply a new variant of the density of states method to the Z3 spin model at finite density. We use restricted expectation values evaluated with Monte Carlo simulations and study their dependence on a control parameter lambda. We show that a sequence of one-parameter fits to the Monte-Carlo data as a function of lambda is sufficient to completely determine the density of states. We expect that this method has smaller statistical errors than other approaches since all generated Monte Carlo data are used in the determination of the density. We compare results for magnetization and susceptibility to a reference simulation in the dual representation of the Z3 spin model and find good agreement for a wide range of parameters.