109 research outputs found
Elliptic solution for modified tetrahedron equations
As is known, tetrahedron equations lead to the commuting family of
transfer-matrices and provide the integrability of corresponding
three-dimensional lattice models. We present the modified version of these
equations which give the commuting family of more complicated two-layer
transfer-matrices. In the static limit we have succeeded in constructing the
solution of these equations in terms of elliptic functions.Comment: 11 page
Generalized Yang-Baxter Equation
A generalization of the Yang-Baxter equation is proposed. It enables to
construct integrable two-dimensional lattice models with commuting two-layer
transfer matrices, while single-layer ones are not necessarily commutative.
Explicit solutions to the generalized equations are found. They are related
with Botzmann weights of the chiral Potts model.Comment: 13 pages, TeX file. IHEP-93-?
Enumeration of quarter-turn symmetric alternating-sign matrices of odd order
It was shown by Kuperberg that the partition function of the square-ice model
related to the quarter-turn symmetric alternating-sign matrices of even order
is the product of two similar factors. We propose a square-ice model whose
states are in bijection with the quarter-turn symmetric alternating-sign
matrices of odd order, and show that the partition function of this model can
be also written in a similar way. This allows to prove, in particular, the
conjectures by Robbins related to the enumeration of the quarter-turn symmetric
alternating-sign matrices.Comment: 11 pages, 13 figures; minor correction
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