84 citations · 428 across the 62 of their papers we have counts for
62 papers
Self-similarity on 4d cubic lattice
Igor G. Korepanov
A phenomenon of "algebraic self-similarity" on 3d cubic lattice, providing what can be called an algebraic analogue of Kadanoff--Wilson theory, is shown to possess a 4d version as…
Solutions to quantum tetrahedron equation with two colors and nonnegative matrix entries
Igor G. Korepanov
In this short note, we construct solutions to quantum tetrahedron equation of the kind "with variables on the edges". Each of these variables takes just two values, called sometime…
Combinatorial correlation functions in three-dimensional eight-vertex models
Igor G. Korepanov
A new version of the self-similarity spin transform on three-dimensional cubic lattices is proposed that makes possible calculation of nontrivial spin correlations in a "combinator…
Heptagon relations from a simplicial 3-cocycle, and their cohomology
Igor G. Korepanov
We introduce new algebraic structures associated with heptagon relations -- higher analogue of the well-known pentagon. The main points we deal with are: (i) polygon relations as a…
Self-similarity in cubic blocks of -operators
Igor G. Korepanov
Cubic blocks are studied assembled from linear operators acting in the tensor product of linear "spin" spaces. Such operator is associated with a linear transforma…
Odd-gon relations and their cohomology
Igor G. Korepanov
A cohomology theory for "odd polygon" relations -- algebraic imitations of Pachner moves in dimensions 3, 5, ... -- is constructed. Manifold invariants based on polygon relations a…