Possible new phase of antagonistic nematogens in a disorienting field

A simple model is proposed for nematogenic molecules that favor perpendicular orientations as well as parallel ones. (Charged rods, for example, show this antagonistic tendency.) When a small disorienting field is applied along z, a low-density phase N- of nematic order parameter S(z)<0 coexists with a dense biaxial nematic N(b). (At zero field, N- becomes isotropic and N(b) uniaxial.) But at stronger fields, a new phase N+4, invariant under pi/2 rotations around the field axis, appears in between N- and N(b). Prospects for finding the N+4 phase experimentally are briefly discussed.