In the homogeneous spin-vector mean-field scheme with field cost and spin-summed density of states per site, the paramagnetic curvature is proportional to . It changes sign at . For a smooth low-temperature density of states, , giving the familiar Fermi-level criterion. Interaction and spin-counting conventions must be specified before comparing coefficients.
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The Stoner criterion is a concept in solid-state physics that provides a condition for the onset of ferromagnetism in materials. It is named after the physicist Edmund C. Stoner, who formulated it in the context of electron spin and magnetic properties in metals. The Stoner criterion can be expressed using the density of states at the Fermi level and the exchange interaction parameter, which reflects the strength of the interaction between electrons with opposite spins.