Criticality in a hadron resonance gas model with the van der Waals interaction

The van der Waals interaction is implemented in a hadron resonance gas model. It is shown that this model can describe lattice QCD data of different thermodynamical quantities satisfactorily with the van der Waals parameters $a=1250\pm 150$ MeV ${\mathrm{fm}}^3$ and $r=0.7\pm 0.05$ fm. Further, a liquid-gas phase transition is observed in this model with the critical point at temperature, $T=62.1$ MeV and baryon chemical potential, ${\mu }_B=708$ MeV.

Figure 1

The variation of different thermodynamical quantities with the temperature at $\mu =0$. Blue lines show the results of VDWHRG model using the parameters $a=1250$ MeV ${\mathrm{fm}}^3$ and $r=0.7$ fm. Blue bands are due to the errors on the van der Waals parameters in the VDWHRG model. The continuum extrapolated LQCD data are taken from Refs. [2] (WB) and [3] (HotQCD).

Figure 2

The variation of second-order fluctuations of conserved charges with the temperature at zero chemical potential. Blue lines show the results of VDWHRG model using the parameters $a=1250$ MeV ${\mathrm{fm}}^3$ and $r=0.7$ fm. Blue bands are due to the errors on the van der Waals parameters in the VDWHRG model. The LQCD data are taken from Refs. [5, 16].

Figure 3

The variation of correlations between conserved charges with the temperature at zero chemical potential. Blue lines show the results of the VDWHRG model using the parameters $a=1250$ MeV ${\mathrm{fm}}^3$ and $r=0.7$ fm. Blue bands are due to the errors on the van der Waals parameters in the VDWHRG model. The LQCD data are taken from Refs. [5, 16].

Figure 4

The variation of pressure with the number density of the hadronic medium at different temperature. The black dot indicates the critical point.

Figure 5

Variations of ${(\partial p/\partial n)}_T$ with respect to ${\mu }_B$ and $n$, respectively.

Figure 6

The critical point of the liquid-gas transition of the present work in the QCD phase diagram. Critical points calculated in lattice are taken from Refs. [81] (Fodor et al.) and [82] (Datta et al.). Chemical freeze-out (CFO) parameters shown in this figure are taken from Refs. [63] (Andronic et al.) and [83] (Cleymans et al.).