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Self-similarity in cubic blocks of R-operators.
- Source :
-
Journal of Mathematical Physics . Oct2023, Vol. 64 Issue 10, p1-21. 21p. - Publication Year :
- 2023
-
Abstract
- Cubic blocks are studied assembled from linear operators R acting in the tensor product of d linear "spin" spaces. Such operator is associated with a linear transformation A in a vector space over a field F of a finite characteristic p, like "permutation-type" operators studied by Hietarinta [J. Phys. A: Math. Gen. 30, 4757–4771 (1997)]. One small difference is that we do not require A and, consequently, R to be invertible; more importantly, no relations on R are required of the type of Yang–Baxter or its higher analogues. It is shown that, in d = 3 dimensions, a pn × pn × pn block decomposes into the tensor product of operators similar to the initial R. One generalization of this involves commutative algebras over F and allows to obtain, in particular, results about spin configurations determined by a four-dimensional R. Another generalization deals with introducing Boltzmann weights for spin configurations; it turns out that there exists a non-trivial self-similarity involving Boltzmann weights as well. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 64
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 173336119
- Full Text :
- https://doi.org/10.1063/5.0143884