Open AccessEigenvalues and eigenvectors of Ising model on hypercube
Author(s) -
Boris Kryzhanovsky,
Leonid Litinskii
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1745/1/012038
Subject(s) - eigenvalues and eigenvectors , ising model , kronecker delta , mathematics , defective matrix , hypercube , matrix (chemical analysis) , connection (principal bundle) , eigenvalues and eigenvectors of the second derivative , matrix differential equation , pure mathematics , mathematical analysis , combinatorics , physics , diagonalizable matrix , symmetric matrix , statistical physics , quantum mechanics , geometry , materials science , composite material
For a multidimensional Ising model, we expressed eigenvalues of the connection matrix in terms of the spin-spin interaction constants and trigonometric polynomials. In such systems, the eigenvectors are the Kronecker products of the well-known eigenvectors for the one-dimensional case. When boundary conditions are periodic, it is possible to obtain rigorous expressions for the eigenvalues when there is an arbitrary long-range interaction in the system.