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In this article we explore the critical end point in the $T-\mu$ phasediagram of a thermomagnetic nonlocal Nambu--Jona-Lasinio model in the weakfield limit. We work with the Gaussian regulator, and find that a crossovertakes place at $\mu, B=0$. The crossover turns to a first order phasetransition as the chemical potential or the magnetic field increase. Thecritical end point of the phase diagram occurs at a higher temperature andlower chemical potential as the magnetic field increases. This result is inaccordance to similar findings in other effective models. We also find there isa critical magnetic field, for which a first order phase transition takes placeeven at $\mu=0$.

Critical end point in a thermo-magnetic nonlocal NJL model