How to locate the QCD phase boundary by scanning observable in the phase plane

TL;DR

This paper proposes a finite-size scaling method using the width of observable points to locate the QCD phase boundary, applicable across critical, transition, and crossover regions in heavy ion collisions.

Contribution

It introduces a novel width-based fixed point analysis to identify the QCD phase boundary from finite-size scaling of observables.

Findings

Contour plots of the width reveal fixed points corresponding to phase transition features.

The method can distinguish critical, transition, and crossover regions.

Demonstrated using Potts model simulations.

Abstract

For small volume of the quark-gluon plasma formed in heavy ion collisions, the observable near criticality must obey finite-size scaling. According to the finite-size scaling, there exists a fixed point at the critical temperature, where scaled susceptibility at different system sizes intersect. It also exists at the transitional temperature of a first order phase transition and can be generalized to the region of the crossover. In order to quantify the feature of the fixed point, we introduce {\it the width of a set of points}. When all points in the set are in their mean position within error, the width reaches its minimum, and all points merge into the fixed point. Using the observable produced by the Potts model, we demonstrate that the contour plot of the width defined in this study clearly indicates the temperatures and exponent ratios of fixed point, which could correspond to either the critical point, the points on the transition line, or the crossover region. This method is therefore instructive to the determination of QCD phase boundary by beam energy scan in relativistic heavy ion collisions.