Remarks on the reweighting method in the chemical potential direction

TL;DR

This paper analyzes the reweighting method in the chemical potential direction, focusing on phase transition shifts and fluctuations, and discusses implications for the sign problem and different chemical potential scenarios.

Contribution

It provides insights into the fluctuation effects of reweighting factors on phase transition lines and compares different approaches to determining critical points.

Findings

Absolute value of reweighting factor influences phase transition shift

Phase fluctuation causes sign problem but minimally affects critical point

Different chemical potential methods yield consistent critical behavior

Abstract

We comment on the reweighting method in the chemical potential $(\mu_{\rm q})$ direction. We study the fluctuation of the reweighting factor during Monte-Carlo steps. We find that it is the absolute value of the reweighting factor that mainly contributes to the shift of the phase transition line $(\beta_c)$ by the presence of $\mu_{\rm q}$. The phase fluctuation is a cause of the sign problem, but the effect on $\beta_c$ seems to be small. We also discuss $\beta_c$ for Iso-vector chemical potential and $\beta_c$ determined from simulations with imaginary chemical potential.