A Clifford algebraic method for the knot structures of 3D-Ising model (Zhang's conjecture)

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