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

Abstract: We introduce a novel eigen-microstate approach to expose critical patterns in relativistic heavy-ion collisions. We explicitly construct the original microstate, defined as the final-state particle fluctuations of a single event. By examining ensembles of such microstates with controlled critical signals, we demonstrate that the approach is highly effective in detecting and quantifying critical patterns, with the largest eigenvalue serving as a robust order parameter. This framework is directly applicable to RHIC Beam Energy Scan data, offering a powerful new direction in the search for the QCD critical point.