Search for the critical endpoint in high-statistics lattice QCD simulations

¹ Department of Physics, Wuppertal University, Gaussstr. 20, D-42119, Wuppertal, Germany
² Department of Physics, Pennsylvania State University, State College, PA 16801, USA
³ Institute for Theoretical Physics, ELTE Eötvös Loránd University, Pázmány P. sétány 1/A, H-1117 Budapest, Hungary
⁴ Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
⁵ Dipartimento di Fisica, Università di Torino and INFN Torino, Via P. Giuria 1, I-10125 Torino, Italy

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 17 April 2026

Abstract

One method to estimate the position of the critical endpoint of QCD is to model the free energy as a rational function of the baryon chemical potential μ_B and determine the Lee-Yang edge singularities. Using high-statistics simulations on 4HEX improved staggered 16³ × 8 lattices by the WuppertalBudapest Collaboration we estimate the location of the closest singularity in the QCD phase diagram. Using this lattice setup we are able to reach an unprece-dentedly low temperature of T = 100 MeV in our simulation dataset. To understand the true predictive power of such an approach, we analyze the systematic uncertainties of such an approach in detail. We compare various ansätze, including formulations that preserve baryon charge quantization by forcing the appropriate periodicity in the imaginary chemical potential. The parameters can be constrained by the cumulants of the net baryon density calculated with lattice simulations at μ_B² ≤ 0. Thus, we also compare single point and multipoint Padé approximations.