Chiral phase transition in the presence of spinodal decomposition

The thermodynamics of a first order chiral phase transition is considered in the presence of spinodal phase separation within the Nambu-Jona-Lasinio (NJL) model. The properties of the basic thermodynamic observables in the coexistence phase are discussed for zero and non-zero quark masses. We focus on observables that probe the chiral phase transition. In particular, the behavior of the specific heat and entropy as well as charge fluctuations are calculated and analyzed. We show that the specific heat and charge susceptibilities diverge at the isothermal spinodal lines. We determine the scaling behavior and compute the critical exponent $\gamma$ of the net quark number susceptibility at the isothermal spinodal lines within the NJL model and the Ginsburg-Landau theory. We show that in the chiral limit the critical exponent $\gamma=1/2$ at the tricritical point as well as along the isothermal spinodal lines. On the other hand, for finite quark masses the critical exponent at the spinodal lines, $\gamma=1/2$, differs from that at the critical end point, $\gamma=2/3$, indicating a change in the universality class. These results are independent of the particular choice of the chiral Lagrangian and should be common for all mean field approaches.