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- Moscow Power Engineering InstituteRU82 papers
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7 papers · 1 filter
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…
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…
Heptagon relation in a direct sum
Igor G. Korepanov
An ansatz is proposed for heptagon relation, that is, algebraic imitation of five-dimensional Pachner move 4--3. Our relation is realized in terms of matrices acting in a direct su…