Isothermal M -H curves, coupled with the critical state model, are routinely used to extract critical current density J c (B); and the limitations and validity are well understood. These hysteretic M -H curves can also be used to estimate the equilibrium magnetization M eq (H), and this paper discusses the validity of such a procedure using analytically tractable models for J c (H). We put special emphasis on the case where the M -H curve shows a fish tail or peak effect, and an experimental

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... cedure to estimate errors in the inferred M eq (H) is presented. The need to infer M eq (H) is underscored by recent experimental works speculating on thermodynamic phase transitions between vortex phases having intrinsic pinning. ͓S0163-1829͑99͒01413-7͔