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An attempt is made to clarify the concept of "spontaneous magnetization" in idealized ferromagnets such as the Ising and Heisenberg models. Some definitions in common use are discussed; their equivalence is not obvious. It is shown that a value based upon the probability distribution of the total magnetization cannot exceed the spontaneous magnetization based on bulk thermodynamic properties when the magnetization and exchange operators commute. A convexity argument shows that a definition of spontaneous magnetization based on minima in the (bulk) free energy is not applicable to systems with short-range interactions. Reference is made to difficulties arising when magnetization and exchange operators do not commute.
Robert B. Griffiths (Fri,) studied this question.