, Volume 22, Issue 3, pp 757-769,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 18 Jul 2012

On the Ternary Approach to Clifford Structures and Ising Lattices


We continue to modify and simplify the Ising-Onsager-Zhang procedure for analyzing simple orthorhombic Ising lattices by considering some fractal structures in connection with Jordan and Clifford algebras and by following Jordan-von Neumann-Wigner (JNW) approach. We concentrate on duality of complete and perfect JNW-systems, in particular ternary systems, analyze algebras of complete JNW-systems, and prove that in the case of a composition algebra we have a self-dual perfect JNW-system related to quaternion or octonion algebras. In this context, we are interested in the product table of the sedenion algebra.