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Eigenvalues of the Transfer Matrix of the Three-Dimensional Ising Model in the Particular Case n = m = 2
- Source :
- Theoretical and Mathematical Physics. 199:909-921
- Publication Year :
- 2019
- Publisher :
- Pleiades Publishing Ltd, 2019.
-
Abstract
- The 16th-order transfer matrix of the three-dimensional Ising model in the particular case n = m = 2 (n × m is number of spins in a layer) is specified by the interaction parameters of three basis vectors. The matrix eigenvectors are divided into two classes, even and odd. Using the symmetry of the eigenvectors, we find their corresponding eigenvalues in general form. Eight of the sixteen eigenvalues related to odd eigenvectors are found from quadratic equations. Four eigenvalues related to even eigenvectors are found from a fourth-degree equation with symmetric coefficients. Each of the remaining four eigenvalues is equal to unity.
Details
- ISSN :
- 15739333 and 00405779
- Volume :
- 199
- Database :
- OpenAIRE
- Journal :
- Theoretical and Mathematical Physics
- Accession number :
- edsair.doi...........4d153552768724a967c4cc51fad165f2