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The quasiclassical limit of the integrable statistical 3D lattice model known as the Zamolodchikov-Bazhanov-Baxter model is considered. We obtain a classical equation of motion for the scalar field, defined on the cubic lattice in 2 + 1 - dimensional space-time, and show that it can be seen as a generalization of the Miwa equations.
Simple solutions of modified tetrahedron equation are given. These solutions are related to the known solutions of the tetrahedron equation. Each R-matrix contains one (or two) spectral parameter(s). Using these simple solutions one gets two (resp. four) parameters commuting sets of two-layer transfer matrices, the whole number of parameters in each two-layer transfer matrix being five (resp...
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