Article
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Spinor Approach for Three-Dimensional Ising Model
Version 1
: Received: 19 September 2023 / Approved: 20 September 2023 / Online: 20 September 2023 (12:32:42 CEST)
How to cite: Zhang, D. Spinor Approach for Three-Dimensional Ising Model. Preprints 2023, 2023091401. https://doi.org/10.20944/preprints202309.1401.v1 Zhang, D. Spinor Approach for Three-Dimensional Ising Model. Preprints 2023, 2023091401. https://doi.org/10.20944/preprints202309.1401.v1
Abstract
The three-dimensional Ising model on the m$\times$n$\times$l cubic lattice with the screw boundary condition along the ${\bf X}$ direction and the periodic boundary conditions along both ${\bf Y}$ and ${\bf Z}$ directions is exactly solved by using the $2^{mn}$-dimensional representation of the rotation group in $2mn$-dimensions, similar to the Kaufman's spinor approach in two dimensions. The exact partition function is obtained from two sets of $2^{mn-1}$ eigenvalues of the $2^{mn}$-dimensional transfer matrix {\bf V} corresponding to the even and odd eigenvectors, respectively. Such the eigenvalues are determined by the angles of the 2mn-dimensional rotation associated with {\bf V}.
Keywords
3D Ising model; Spinor approach; Partition function
Subject
Physical Sciences, Thermodynamics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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