Interpolating the Free Energy Density Differences of Reweighting Methods

TL;DR

This paper addresses the overlap problem in reweighting methods for fermionic systems, proposing an interpolation approach to accurately evaluate critical phenomena, demonstrated on QCD with four flavors.

Contribution

It introduces a new interpolation technique to map joint ratio distributions, improving the evaluation of critical lines in fermionic systems.

Findings

Successfully applied to QCD with four flavors

Provides criteria for accurate ratio distribution mapping

Enhances understanding of reweighting overlap issues

Abstract

A discussion of the overlap problem of reweighting approaches to evaluating critical phenomenon in fermionic systems is motivated by highlighting the divergence of the joint probability density function of a general ratio. By identifying the bounds for which this integral can be expressed in closed form, we establish criteria for accurately mapping the joint ratio distribution of two disjoint ensembles through interpolation. The approach is applied to QCD with four staggered flavours to evaluate the critical line in the $\beta-\mu$ plane.