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 $H={-}{Σ}{i,j}^{}{J}ᵢⱼ{{{→}}{S}}ᵢ·{}{{{→}}{S}}ⱼ+{Σ}{i,j}^{}({J}ᵢⱼ{-}{K}ᵢⱼ){S}ᵢˣ{S}ⱼˣ$, 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.