Critical behavior of Binder ratios and ratios of higher order cumulants of conserved charges in QCD deconfinement phase transition

TL;DR

This paper investigates the critical behavior of Binder ratios and higher order cumulant ratios of conserved charges in QCD phase transitions using the 3D-Ising model, revealing characteristic patterns near the critical point.

Contribution

It provides a detailed analysis of the critical behavior of Binder ratios and cumulant ratios in the 3D-Ising model, offering new insights for locating the QCD critical point in heavy ion collisions.

Findings

Binder ratio is a step function of temperature.

Ratios of third order cumulants change from negative to positive across the critical point.

Ratios of fourth order cumulants oscillate around zero.

Abstract

Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. Using 3D-Ising model, the critical behavior of Binder ratios and ratios of high order cumulants of order parameter are fully presented. Binder ratio is shown to be a step function of temperature. The critical point is the intersection of the ratios of different system sizes between two platforms. From low to high temperature through the critical point, the ratios of third order cumulants change their values from negative to positive in a valley shape, and ratios of fourth order cumulants oscillate around zero. The normalized ratios, like the Skewness and Kurtosis, do not diverge with correlation length, in contrary with corresponding cumulants. Applications of these characters in search critical point in relativistic heavy ion collisions are discussed.