Ising parameterization of QCD Landau free energy and its dynamics.

We present a general linear parameterization scheme for the QCD Landau free energy in the vicinity of the critical point of chiral phase transition in the $\mu$-$T$ plane. Based on the parametric free energy, we show that, due to the finite size effects, the regions of fluctuations of the order parameter (i.e. the $\sigma$ field) are broadened, and the discontinuities of the first order phase transition are smoothed. Meanwhile, the kurtosis of the $\sigma$ field is universally negative around the critical point. Using the Fokker-Plank equation, we derive the dynamical corrections to the free energy. The dynamical cumulants of the $\sigma$ field on the freeze-out line, record earlier information in the first order phase transition region as compared to the crossover region. The typical behavior of dynamical cumulants can be understood from the equilibrium cumulants by considering the memory effects.