Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems

TL;DR

This paper investigates the non-commutativity between the zero chemical potential limit and the thermodynamic limit in finite density systems, revealing implications for Monte Carlo simulations and reweighting techniques.

Contribution

It demonstrates the non-commutativity in finite density systems using a Random Matrix Theory model and explains how the factorization method addresses this issue.

Findings

Non-commutativity affects intermediate calculation steps.

Factorization method cancels non-commutativity in final results.

Implications for Monte Carlo simulations at finite density.

Abstract

Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain non-commutativity in the zero chemical potential limit and the thermodynamic limit when one tries to study such systems by reweighting techniques. This is demonstrated by explicit calculations in a Random Matrix Theory, which is thought to be a simple qualitative model for finite density QCD. The factorization method allows us to understand how the non-commutativity, which appears at the intermediate steps, cancels in the end results for physical observables.