Orientational ordering transition in a continuous-spin ferrofluid

We have considered a classical system, consisting of particles with centre-of-mass coordinates x Rd and equipped with a one-component spin σx R1; their pairwise additive interaction potential is defined by W(x,σx,y,σy)=Φ( x−y )−J( x−y )σxσy , where Φ( x−y ) contains a hard-core term and J( x−y ) 0. We prove the existence of orientational long-range order (magnetization) for large chemical potentials and low temperatures, when d 2; the same result holds for d=1 and long-range ferromagnetic interactions. Our general model can be realized by extremely anisotropic interaction potentials involving continuous multi-component spins, where only one component is involved in the coupling.