Article
Version 1
Preserved in Portico This version is not peer-reviewed
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.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment