Critical points in the linear σ model with quarks

We employ a simple effective model to study the chiral dynamics of two flavors of quarks at finite temperature and density. In particular, we determine the phase diagram in the plane of temperature and baryon chemical potential as a function of the pion mass. An interesting phase structure occurs that results in zero, one, or two critical points depending on the value of the vacuum pion mass.

Figure 1

Pressure vs baryon chemical potential for two different temperatures with the physical value of the pion mass in vacuum. At the lower temperature there is a discontinuity in the slope at the crossing point, indicating a first-order phase transition. The curves are extended to the limits of metastability. At the higher temperature the pressure is smooth and there is no phase transition.

Figure 2

The energy density, normalized to $T^4$, vs $T$ at zero chemical potential. For zero vacuum pion mass there is a first-order transition, whereas for a vacuum pion mass of 200 MeV there is only a rapid crossover.

Figure 3

Phase diagram of this model for illustrative values of the vacuum pion mass. The solid curves represent a first-order phase transition, terminating at a critical point where the transition is second order. For zero vacuum pion mass the curve is first order all the way from one axis to the other.

Figure 4

Phase diagram of this model for a vacuum pion mass of 35 MeV. The solid curves represent a first-order phase transition, terminating at a critical point where the transition is second order. For this value of the vacuum pion mass there are two critical points.

Figure 5

Latent heat along the critical curve for various vacuum pion masses. The critical point corresponds to the vanishing of the latent heat. Note that for a vacuum pion mass of 35 MeV there is a second region in the bottom right corner.