Ising-like dynamical signatures and the end point of the QCD transition line

An increase in the size of coherent domains in the one component ${\ensuremath{\Phi}}^{4}$ field theory under the influence of a uniformly changing external magnetic field near the critical end point ${T}_{\ensuremath{\Phi}}{=T}_{c}{,h}_{\ensuremath{\Phi}}=0$ was proposed recently as an estimate also for the variation of the chiral correlation length of QCD near its respective hypothetical end point in the ${T}_{\mathrm{QCD}}\ensuremath{-}{\ensuremath{\mu}}_{\mathrm{QCD}}$ plane. The present detailed numerical investigation of the effective model suggests that passing by the critical QCD end point with a realistic rate of temperature change will trigger large amplitude oscillations in the temporal variation of the chiral correlation length. A simple mechanism for producing this phenomenon is suggested.