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Inverse magnetic catalysis and confinement within a contact interaction model for quarks

We evaluate the impact of an external magnetic field on the chiral symmetry and confinement-deconfinement transition temperatures by using a vector-vector contact interaction model for quarks regularized so as to include an explicit confining scale in the corresponding gap equation. Exploring the evolution of the chiral condensate and the confining scale with temperature $T$ and magnetic field strength $eB$ ($e$ represents the fundamental electric charge), we determine the pseudo-critical temperatures for the chiral ($T_c^χ$) and deconfinement ($T_c^c$) transitions from their inflection points, respectively. By construction, $T_c^χ= T_c^c$ in the chiral limit. Within a mean field approximation, we observe the magnetic catalysis phenomenon, characterized by a rising behavior of $T_c^χ$ and $T_c^c$ with growing $eB$. Considering a lattice inspired running coupling which monotonically decreases with $eB$, inverse magnetic catalysis takes place in our model. We explore the role of the magnetic field in the traits of the confinement-deconfinement transition described by the model. Our findings are also in agreement with predictions derived from effective models of strong interactions.