We consider the ground state of a system of chargeless fermions, such as neutrinos, of mass m and magnetic moment m interacting through long-range magnetic dipole interaction, within the framework of a {Hartree-Fock} variational approach. At high densities the uniform paramagnetic state becomes unstable towards a ferromagnetic state with quadrupolar deformation of the Fermi surface. The exchange energy which is attractive dominates the repulsive kinetic energy. If we let the density be a variable, then above a certain density the system will collapse to an infinite density state unless another short-range interaction stops the collapse. In the case of large deformations, the possibility of a purely dipolar deformation exists.

%B Journal of Physics A: Mathematical and General %V 39 %P 1239–1249 %8 02/2006 %G eng %N 6