Ising-QCD phenomenology close to the critical point

We employ the recently introduced Ising-QCD partition function (N.~G. Antoniou {\it et al.}, Phys. Rev. D 97, 034015 (2018)) to explore in detail the behaviour of the moments of the baryon-number, within the critical region around the critical endpoint. Our analysis is based on the relation of finite-size scaling in real space with intermittency in transverse momentum space. It demonstrates in practice the recent observation (N.~G. Antoniou {\it et al.}, Phys. Rev. D 97, 034015 (2018)) that combined measurements of the intermittency index $\phi_2$ and the freeze-out parameters $\mu_b$ (baryochemical potential), $T$ (temperature), provide us with a powerful tool to detect the critical point. We also show that the finite-size scaling (FSS) region, as a part of the critical region, is very narrow in both the chemical potential and the temperature direction, even for light nuclei. Furthermore, using published experimental results for $(\mu_b,T,\phi_2)$ in A+A collisions at $\sqrt{s_{NN}}=17.2$ GeV (NA49 experiment, CERN-SPS), we are able to make a set of predictions for the freeze-out states of Ar + Sc and Xe + La collisions at the same energy in the NA61/SHINE experiment (CERN-SPS). In particular, we find that the Ar + Sc system freezes out outside the FSS region but very close to its boundary, a property which may leave characteristic traces in intermittency analysis.