ICCA10

Tartu, 4–9 August 2014

10^{th} International Conference on Clifford Algebras and their Applications in Mathematical Physics

Presenter: **Osamu Suzuki**, Department of Compute rand System Analysis College of Humanities and Sciences, Nihon University, Japan

Joint work with **Zhang-Zhindong**

The non-trivial knot or link structure will be expected to be observed in 3D-Ising model. The structure makes the difference between 2D-Ising model and 3D-Ising model. The second author has made a conjecture on the structure ([1]). In this talk, we propose a method of analysis by use of Clifford algebra and give a description of the structure in terms of Clifford algebra. Then applying the methods of Riemann-Hilbert problem on Riemann surface and monoidal transform, we will discuss the conjecture and show the its possibility ([2]). Details will be given in the forthcoming paper.

[1] Z.-D.Zhang. *Conjecture on the exact solution of three-dimensional (3D) simple orthorthombic Ising lattices*, Philosophical Magazine, Vol. 87, Nos. 34-36, 1-21 December 2007, 5309-5419

[2] H. Roehl. *Das Riemannsch-Hilbertsche Problem der Theorie der linearen Differentialgleichungen*, Math. Ann., 133 (1957), 1-25