Eigen-microstate Signatures of Criticality in Relativistic Heavy-Ion Collisions

Abstract

We develop the eigen-microstate framework as a new approach to identify criticality in relativistic heavy-ion collisions. We construct the original microstate, defined as the final-state particle fluctuations of a single event. By examining ensembles of such original microstates with and without critical signals, we demonstrate that the corresponding eigen-microstate can extract and reveal the dominant critical mode, with the largest eigenvalue serving as a robust order parameter. This framework avoids equilibrium assumptions and is insensitive to non-critical background, and the approach is directly applicable to RHIC Beam Energy Scan data, offering a powerful new tool in the search for the QCD critical point.

Figures (3)

• Figure 1: An original microstate (first column) and the top three eigen microstates (columns 2--4) for the UrQMD sample (first row) and corresponding hybrid UrQMD$+$CMC samples with critical-signal fractions $\alpha_{\rm p}=6$%, 9%, and 12% (rows 2--4) at $L=60$.
• Figure 2: (a) Top three weights $w_{1,2,3}$ as functions of signal fraction $\alpha_{\rm p}$ for $L=60$. (b) Weight cumulants for the original UrQMD sample and hybrid UrQMD$+$CMC samples with $\alpha_{\rm p}=20\%$ and $70\%$.
• Figure 3: Top three eigen microstates for hybrid UrQMD$+$CMC samples with $\alpha_{\rm p}=70\%$ at $L=10$, 40, and 100.