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A system of spins on a lattice with magnetic dipole-dipole interactions, exchange, and anisotropy forces is shown to possess a well-defined bulk free energy, independent of sample shape, in the thermodynamic limit, provided there is no external magnetic field. The proof applies to classical or quantum spin systems with arbitrary g tensors, and is independent of any assumption of order or disorder in the magnetic phase, convergence of perturbation series, etc.
Robert B. Griffiths (Tue,) studied this question.