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First order transition region of an equation of state for QCD with a critical point

Jamie M. Karthein, Volker Koch, Claudia Ratti

TL;DR

The work investigates whether a QCD critical point exists and how a first-order transition would manifest in the QCD phase diagram. It adopts a mean-field Ising model equation of state mapped linearly onto QCD variables to construct the full first-order region, including coexistence and spinodal lines, while enforcing lattice-QCD constraints to reduce parameter freedom; the analysis is illustrated with a chosen critical point at $\mu_{B,c}=550$ MeV. The key contribution is an analytically tractable equation of state that describes both coexistence and spinodal regions, including metastable and unstable sectors, with pressure–density behavior suitable for hydrodynamic simulations of low-energy heavy-ion collisions, and a comparison to 3D Ising-based EOS approaches. Overall, the framework enables indirect probing of the critical point through the structure of the first-order region and provides a practical tool for studying spinodal phenomena in the QCD phase diagram.

Abstract

In addition to signals for the critical point, evidence for a first order phase transition would indicate a nontrivial structure within the QCD phase diagram. Moreover, while not a direct measurement of the critical point, the presence of a first order transition would imply its existence. This motivates the need to understand signatures of this first order transition in addition to directly studying the effect of a critical point. To this effect, we map the mean-field Ising model equation of state onto the QCD phase diagram, and reconstruct the full coexistence region in the case of a first order phase transition. Beyond the coexistence line, we maintain access to the spinodal region in the phase diagram, thus providing a description of metastable and unstable phases of matter. Thus, we describe the super-heated hadronic phase and the super-cooled quark-gluon plasma, which is useful for hydrodynamic simulations of the fireball created in a heavy-ion collision at low collision energy, where a first order phase transition is expected. We discuss the features of the pressure and other thermodynamic observables as functions of temperature and baryonic chemical potential, in particular their behavior in the coexistence region. Finally, we compare our equation of state to 3D Ising model ones available in the literature.

First order transition region of an equation of state for QCD with a critical point

TL;DR

The work investigates whether a QCD critical point exists and how a first-order transition would manifest in the QCD phase diagram. It adopts a mean-field Ising model equation of state mapped linearly onto QCD variables to construct the full first-order region, including coexistence and spinodal lines, while enforcing lattice-QCD constraints to reduce parameter freedom; the analysis is illustrated with a chosen critical point at MeV. The key contribution is an analytically tractable equation of state that describes both coexistence and spinodal regions, including metastable and unstable sectors, with pressure–density behavior suitable for hydrodynamic simulations of low-energy heavy-ion collisions, and a comparison to 3D Ising-based EOS approaches. Overall, the framework enables indirect probing of the critical point through the structure of the first-order region and provides a practical tool for studying spinodal phenomena in the QCD phase diagram.

Abstract

In addition to signals for the critical point, evidence for a first order phase transition would indicate a nontrivial structure within the QCD phase diagram. Moreover, while not a direct measurement of the critical point, the presence of a first order transition would imply its existence. This motivates the need to understand signatures of this first order transition in addition to directly studying the effect of a critical point. To this effect, we map the mean-field Ising model equation of state onto the QCD phase diagram, and reconstruct the full coexistence region in the case of a first order phase transition. Beyond the coexistence line, we maintain access to the spinodal region in the phase diagram, thus providing a description of metastable and unstable phases of matter. Thus, we describe the super-heated hadronic phase and the super-cooled quark-gluon plasma, which is useful for hydrodynamic simulations of the fireball created in a heavy-ion collision at low collision energy, where a first order phase transition is expected. We discuss the features of the pressure and other thermodynamic observables as functions of temperature and baryonic chemical potential, in particular their behavior in the coexistence region. Finally, we compare our equation of state to 3D Ising model ones available in the literature.

Paper Structure

This paper contains 3 sections, 2 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Spinodals in the QCD Phase Diagram
  3. Acknowledgments

Figures (2)

  • Figure 1: The spinodal and coexistence curves on the QCD phase diagram as mapped from the mean field Ising model for a choice $\mu_{B,c}=550$ MeV.
  • Figure 2: An isothermal curve ($T=0.98 T_c$) for the Ising model pressure as a function of the density. The coexistence points are indicated with the open green circles, while the spinodal points are given by the filled orange circles.