Model Study of Eigen-Microstate Signatures of Criticality in Relativistic Heavy-Ion Collisions

TL;DR

This paper introduces an eigen-microstate approach (EMA) for detecting critical fluctuations in relativistic heavy-ion collisions, demonstrating its robustness and scale-invariance in identifying critical phenomena.

Contribution

The study develops and validates EMA as a background-independent method for critical point detection, capturing fractal critical fluctuations across scales.

Findings

EMA filters out non-critical backgrounds effectively.

Eigen-microstates reveal fractal patterns of critical fluctuations.

Largest eigenvalue acts as an order-parameter-like indicator.

Abstract

We present a comprehensive model study of the eigen-microstate approach (EMA) for identifying critical fluctuations in relativistic heavy-ion collisions. Using UrQMD and two stochastic baseline models, we demonstrate that EMA is insensitive to conventional short-range correlations and effectively filters out non-critical backgrounds. Critical fluctuations embedded via event-level or particle-level replacement with CMC events generate characteristic cluster-like eigen-microstate patterns and enhanced leading eigenvalues, with event-level criticality producing stronger responses. The eigen microstates exhibit the same pattern across different scales, demonstrating that the fractal nature of critical fluctuations is captured by the eigen microstates. Finite-size scaling of eigenvalue ratios exhibits fixed-point behavior, confirming the largest eigenvalue as an effective order-parameter-like quantity. These results demonstrate that EMA offers a robust and background-independent method for critical-point searches in the RHIC Beam Energy Scan and future heavy-ion experiments.