Phase polarity in a ferrofluid monolayer of shifted-dipole spheres

We consider a model for ferrofluids in which the constituent colloidal particles are spheres on a
monolayer, with centers freely gliding on a given plane and permanent, point dipoles located along a
radius in each sphere, oriented away from its center and freely pointing in all directions in space. Small
clusters of these particles, also called shifted-dipole spheres in short, were studied in Kantorovich et al.,
Soft Matter, 2011, 7, 5217 to describe the effect of the dipole’s shift on the ground state arrangement of
particles in clusters of different populations at zero temperature. Our approach is somehow
complementary to that; in the limit of many particles, we introduce an average Hamiltonian, in terms of
which we construct a mean-field theory for a homogeneous ferrofluid monolayer. In an appropriate
range of dipole’s shifts, we predict a transition from the isotropic, non-polar phase to an ordered, polar
phase with macroscopic polarization in the plane of the layer, at a critical reduced temperature, which
turns out to be independent of the dipole’s shift.