Abstract
We show that the value of the spontaneous magnetization for the two-dimensional Ising model computed by Onsager is indeed, the appropriate derivative of the free energy with respect to the magnetic field. The argument is based on a simple application of the duality transformation.
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In this appendix for convenience of the reader we give a treatment of duality suitable for the purpose of the present paper. It should be mentioned however, that it contains certain remarks on the role of boundary conditions which do not appear in full detail elsewhere in the literature. For recent formulations of duality in the case of more general models see Wegner, F. J.: J. Math. Phys.12, 2259 (1971); — Merlini, D., Gruber, C.: preprint (1972).
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Benettin, G., Gallavotti, G., Jona-Lasinio, G. et al. On the Onsager-Yang-Value of the spontaneous magnetization. Commun.Math. Phys. 30, 45–54 (1973). https://doi.org/10.1007/BF01646687
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DOI: https://doi.org/10.1007/BF01646687