ИСТИНА

The integrability in statistical physics models is usually expressed in the fact that the statistical sum can be represented via a transfer matrix included in a "large" commutative family. The latter property for two-dimensional models is traditionally accompanied by the structure of the vertex model with the weight matrix satisfying the Yang-Baxter equation. The report will focus on the generalization of this idea to a large dimension, in particular, I will consider the three-dimensional Ising model as well as the Hopfield neural network model on a 2-dimensional triangular lattice in the recalling phase. It turns out that both of these models have a vertex representation with a weight matrix satisfying the deformations of the Zamolodchikov tetrahedron equation. In both cases the hypercube combinatorics is essentially used to construct the weight matrix.