The non-Riemannian geometry of macroscopic spin distributions in thermodynamics and ferromagnetism is obtained from the respective partition functions. An expression for the Cartan torsion in terms of the chemical potential is obtained. Analogies with the Einstein-Cartan theory of gravitation are discussed. From the partition function of ferromagnetism a spin-torsion relation analogous to the one obtained in Einstein-Cartan theory is given where piezomagnetic effects are taken into account.
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