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An increase in the size of coherent domains in the one component $\Phi^4$field theory under the influence of a uniformly changing external magneticfield near the critical end-point $T_{\Phi}=T_c, h_{\Phi}=0$ was proposedrecently as an estimate also for the variation of the chiral correlation lengthof QCD near its respective hypothetical end point in the $T_{QCD}-\mu_{QCD}$plane. The present detailed numerical investigation of the effective modelsuggests that passing by the critical QCD end point with realistic rate oftemperature change will trigger large amplitude oscillations in the temporalvariation of the chiral correlation length. A simple mechanism for producingthis phenomenon is suggested.Comment: 10 pages, RevTeX, 5 figures. Version accepted for publication in PR

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