Comment on "Long-ranged orientational order in dipolar fluids"

Recently Groh and Dietrich[1] calculated orientational order transitions for dipolar fluids contained in spheroidal shapes of aspect ratio k. According to their study the thermodynamic state of a dipolar fluid depends on the shape of the fluid's container. For example, a homogeneous fluid in a short fat container would phase separate when transferred to a tall skinny container of identical volume and temperature. Their calculation thus lacks a thermodynamic limit. Existence of a thermodynamic limit for dipolar fluids has never been proven. Indeed, the long range anisotropic dipole interaction presents significant difficulties. These include mathematical difficulties such as the conditionally convergent, shape dependent integrals examined by Groh and Diet-rich. Physically, the long interaction range causes domain or texture formation to avoid demagnetizing fields. Still, Griffiths[2] has proven the existence of a shape independent thermodynamic limit for the free energy of dipoles on lattices. So we presume that dipolar fluids also possess a thermodynamic 1