Towards integrable structure in 3d Ising model
In this paper, we proceed to the study of tetrahedral symmetry in the 3D Ising model, which is considered as the first forerunner of integrability. The weight matrix of the model on a regular cubic lattice satisfying the twisted tetrahedron equation (TTE) is constructed. The latter is a modification of the Zamolodchikov tetrahedron equation, which appeared in integrable 3D statistical models. The method is based on the theory of the n-simplicial complex and the original recursion procedure on the space of n-simplex solutions. This recursion deserves its own investigation. Surprisingly, the weight matrix has some properties inherent for the hypercube combinatorics and coding theory.