We obtained analytically eigenvalues of a multidimensional Ising Hamiltonian on a hypercube lattice and expressed them in terms of spin-spin interaction constants and the eigenvalues of the one-dimensional Ising Hamiltonian (the latter are well known). To do this we wrote down the multidimensional Hamiltonian eigenvectors as the Kronecker products of the eigenvectors of the one-dimensional Ising Hamiltonian. For periodic boundary conditions, it is possible to obtain exact results taking into account interactions with an unlimited number of neighboring spins. In this paper, we present exact expressions for the eigenvalues for the planar and cubic Ising systems accounting for the first five coordination spheres (that is interactions with the nearest neighbors, the next neighbors, the next-next neighbors, the next-next-next neighbors and the next-next-next-next neighbors). In the case of free-boundary systems, we showed that in the two- and three-dimensions the exact expressions could be obtained only if we account for interactions with spins of first two coordination spheres and first three coordination spheres, respectively.
Low-temperature transition of 2d random-bond Ising model and quantum infinite randomness
Stanford University（斯坦福大学）；All Souls College, Oxford（牛津大学万灵学院）；University of Oxford（牛津大学）；National Institute for Theory and Mathematics in Biology（生物理论与数学国家研究所）；Syracuse University（雪城大学）
Spectral theory of energy-selective quantum search with Ising Hamiltonian phase oracles
Dukhov Research Institute of Automatics (VNIIA)（杜霍夫自动技术研究院）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences（俄罗斯科学院理论与应用电动力学研究所）
