Low-Temperature Behavior of the Planar Heisenberg Ferromagnet

We have examined the low-temperature properties of the cubic-planar Heisenberg ferromagnet with nearest-neighbor exchange which is defined by the Hamiltonian H=-Σi,jJ_ijS⃗_i·S⃗_j+Σi,j(J_ij-K_ij)S_i^xS_j^x, where -J≤K≤J (J positive). We find that as the exchange-anisotropy parameter θ=(J-K)/J ranges over the planar ferromagnetic stability limits 0≤θ≤2, the behavior of the system changes from that of the isotropic ferromagnet at θ=0 into that of the isotropic antiferromagnet at θ=2. The system's noninteracting-spin-wave frequency, ground-state energy, zero-point spin deviation, and lowest-order renormalized frequency scale between isotropic ferromagnetic and antiferromagnetic values as θ goes from zero to two. Over most of the system's stability range, the planar ferromagnet exhibits a mixture of properties combining characteristics of its intrinsic ferromagnetism with those of the antiferromagnet. This behavior is discussed in terms of an isomorphic mapping symmetry for nearest-neighbor exchange in loose-packed lattices which requires that in the limit θ=2 the planar ferromagnet be unitarily equivalent to the isotropic antiferromagnet.