Critical point signatures in the cluster expansion in fugacities

TL;DR

This paper investigates the signatures of critical points in the cluster expansion of baryon density in QCD, analyzing Fourier coefficients to identify phase transition features and applying the method to lattice QCD data.

Contribution

It introduces a method to detect critical points via Fourier coefficients of the cluster expansion in QCD and demonstrates its effectiveness with models and lattice data.

Findings

Fourier coefficients exhibit qualitative changes across the critical temperature.

The closest branch point to the imaginary chemical potential axis can be identified through exponential suppression analysis.

The approach is validated with both toy models and lattice QCD data.

Abstract

The QCD baryon number density can formally be expanded into a Laurent series in fugacity, which is a relativistic generalization of Mayer's cluster expansion. We determine properties of the cluster expansion in a model with a phase transition and a critical point at finite baryon density, in which the Fourier coefficients of the expansion can be determined explicitly and to arbitrary order. The asymptotic behavior of Fourier coefficients changes qualitatively as one traverses the critical temperature and it is connected to the branch points of a thermodynamic potential associated with the phase transition. The results are discussed in the context of lattice QCD simulations at imaginary chemical potential. We argue that the location of a branch point closest to the imaginary chemical potential axis can be extracted through an analysis of an exponential suppression of Fourier coefficients. This is illustrated using the four leading coefficients both in a toy model as well as by using recent lattice QCD data.