Abstract:
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.
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