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In this article we study a nonlocal Nambu--Jona-Lasinio (nNJL) model with aGaussian regulator in presence of a uniform magnetic field. We take a mixedapproach to the incorporation of temperature in the model, and consider aspectsof both real and imaginary time formalisms. We include confinement in the modelthrough the quasiparticle interpretation of the poles of the propagator. Theeffect of the magnetic field in the deconfinement phase transition is thenstudied. It is found that, like with chiral symmetry restoration, magneticcatalysis occurs for the deconfinement phase transition. It is also found thatthe magnetic field enhances the thermodynamical instability of the system. Wework in the weak field limit, i.e. $(eB)<5m_\pi^2$. At this level there is nosplitting of the critical temperatures for chiral and deconfinement phasetransitions.

Thermo-magnetic nonlocal NJL model in the real and imaginary time formalisms