# Universality of the critical point mapping between Ising model and QCD at small quark mass

## TL;DR

This paper demonstrates that near the critical point in QCD with small quark masses, the mapping to the Ising model exhibits universal behavior, especially in the dependence of the mapping parameters on the quark mass.

## Contribution

It reveals that the mapping parameters between QCD and the Ising model become universal functions of quark mass near the tricritical point, with specific geometric implications.

## Key findings

- Mapping parameters depend universally on quark mass as $m_q^{2/5}$
- The angle between critical lines vanishes as quark mass approaches zero
- Universal behavior emerges near the tricritical point in small quark mass limit

## Abstract

The universality of the QCD equation of state near the critical point is expressed by mapping pressure as a function of temperature $T$ and baryon chemical potential $\mu$ in QCD to Gibbs free energy as a function of reduced temperature $r$ and magnetic field $h$ in the Ising model. The mapping parameters are, in general, not universal, i.e., determined by details of the microscopic dynamics, rather than by symmetries and long-distance dynamics. In this paper we point out that in the limit of small quark masses, when the critical point is close to the tricritical point, the mapping parameters show universal dependence on the quark mass $m_q$. In particular, the angle between the $r=0$ and $h=0$ lines in the $(\mu,T)$ plane vanishes as $m_q^{2/5}$. We discuss possible phenomenological consequences of these findings.