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We develop a new approach for sketching the quantum chromodynamicsphase-diagram within the Nambu--Jona-Lasinio model for arbitrarily large valuesof the coupling constant, temperature and chemical potential based upon thestrategy of Lagrange multipliers that constrains the corresponding gap equationand its mass gradient. Our approach distinguishes continuous fromdiscountinuous phase transitions and thus is capable of locating the positionof the Critical End Point from the thermodynamical parameters of the modelalone, without direct reference to the chiral susceptibility or any otherobservable. The approach can be straightforwardly extended to those effectivechiral quark models with a momentum independent constituent quark mass.

An innovative approach for sketching the QCD phase diagram within the NJL model using Lagrange Multipliers