Paul Federbush For the Quantum Heisenberg Ferromagnet, Some Conjectured Approximations (11K, LaTeX) ABSTRACT. We present two conjectured approximations for spin expectations in a Quantum Heisenberg system. The conjectures are based on numerical experimentation, some theoretical insights and underpinning, and aestheticvalue. We hope theoretical developments will follow from these ideas, even leading to a proof of the phase transition (in three dimensions).