Geodesic
Hidden symmetry of free fermion model. III. Inversion relations
Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 3, pp. 417-427 
V. V. Bazhanov; Yu. G. Stroganov. Hidden symmetry of free fermion model. III. Inversion relations. Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 3, pp. 417-427. http://geodesic.mathdoc.fr/item/TMF_1985_63_3_a9/
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It is shown that the partition functions of the free fermion model on a planar lattice satisfies inversion relations, i.e. if the relativistic factorized $S$ matrix corresponding to the model is unitary, the partition function is equal to unity. Further, it is shown that this property also holds for the special case of the free fermion model on a threedimensional cubic lattice. The connection between the results obtained and the unitarization of the $S$ matrix in Zamolodchikov's three-dimensional model is discussed.

[1] Bazhanov V. V., Stroganov Yu. G., TMF, 62:3 (1985), 377–387 | MR

[2] Bazhanov V. V., Stroganov Yu. G., TMF, 63:2 (1985), 291–302 | MR

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[4] Zamolodchikov A. B., Sov. Sci. Rev., 2 (1980), 1–29

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