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We investigate the combined finite-size and thermo-magnetic effects on theproperties of the quark matter, in the context of the two-flavoredNambu--Jona-Lasinio model. In particular, by using the mean-field approximationand the Schwinger proper time method in a toroidal topology with periodic orantiperiodic conditions, we evaluate the chiral phase transition, theconstituent quark mass and the thermal and spatial susceptibilities under thechange of the size, temperature and strength of external magnetic field. Totake into account the inverse magnetic catalysis phenomenon, we make use of arecently proposed magnetized coupling constant. The findings suggest that theobservables are strongly affected by the variation of the variables and also bythe periodicity of the boundary conditions, with the final outcomes dependingon the balance of these competing phenomena.

Inverse magnetic catalysis and size-dependent effects on the chiral symmetry restoration