Interpolating the Free Energy Density Differences of Reweighting Methods

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.