  Using fundamental measure density functional theory we investigate
paranematic-nematic and nematic-nematic phase coexistence in binary mixtures of
circular platelets with vanishing thicknesses. An external magnetic field
induces uniaxial alignment and acts on the platelets with a strength that is
taken to scale with the platelet area. At particle diameter ratio lambda=1.5
the system displays paranematic-nematic coexistence. For lambda=2, demixing
into two nematic states with different compositions also occurs, between an
upper critical point and a paranematic-nematic-nematic triple point. Increasing
the field strength leads to shrinking of the coexistence regions. At high
enough field strength a closed loop of immiscibility is induced and phase
coexistence vanishes at a double critical point above which the system is
homogeneously nematic. For lambda=2.5, besides paranematic-nematic coexistence,
there is nematic-nematic coexistence which persists and hence does not end in a
critical point. The partial orientational order parameters along the binodals
vary strongly with composition and connect smoothly for each species when
closed loops of immiscibility are present in the corresponding phase diagram.
