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.