Scaling region of the 3D Ising universality class in finite temperature QCD

TL;DR

This paper develops a universal framework based on susceptibility and correlation length in the 3D Ising model to identify the critical scaling region, aiding the study of finite temperature QCD phase transitions.

Contribution

It introduces a universal combination of observables and a reference framework for the scaling region in the 3D Ising universality class, applied to finite temperature QCD.

Findings

Defines a universal susceptibility-correlation length combination

Provides a parametric representation of the equation of state near criticality

Facilitates comparison of experimental QCD data with theoretical predictions

Abstract

We introduce a universal combination of susceptibility and correlation length in the 3D Ising model, depending both on temperature and external magnetic field. Starting from a parametric representation of the equation of state, we study its behaviour close to the critical point. The results we derive can be used as a sort of "reference frame" to chart the scaling region of the 3D Ising universality class. More specifically, we focus on instances of Ising behaviour in finite temperature QCD and, among these, we are particularly interested on the critical ending point in the finite density, finite temperature QCD phase diagram. In this context, Monte Carlo simulations are not possible and it is particularly difficult to disentangle "magnetic-like" from "thermal-like" observables, thus an explicit charting of the critical region could be useful for a direct comparison of experimental results with QFT/Statmech predictions.