Towards integrable structure in 3d Ising model
Dmitry V. Talalaev
TL;DR
This paper introduces a weight matrix for the 3D Ising model that satisfies the twisted tetrahedron equation, leveraging n-simplicial complex theory and recursion, revealing properties related to hypercube combinatorics.
Contribution
It constructs a novel weight matrix for the 3D Ising model satisfying a key integrability condition using advanced combinatorial and algebraic methods.
Findings
Weight matrix satisfies the twisted tetrahedron equation.
Reveals properties intrinsic to hypercube combinatorics.
Introduces a recursion procedure on n-simplex solutions.
Abstract
We construct a weight matrix for the 3D Ising model satisfying the so-called twisted tetrahedron equation. The result is based on the theory of the n-simplicial complex and the invented recursion procedure on the space of n-simplex solutions in correspondences. The weight matrix reveals some properties intrinsic for the hypercube combinatorics.
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