Inverse Problem for Ising Connection Matrix with Long-Range Interaction

Abstract

In the present paper, we examine Ising systems on d-dimensional hypercube lattices and solve an inverse problem where we have to determine interaction constants of an Ising connection matrix when we know a spectrum of its eigenvalues. In addition, we define restrictions allowing a random number sequence to be a connection matrix spectrum. We use the previously obtained analytical expressions for the eigenvalues of Ising connection matrices accounting for an arbitrary long-range interaction and supposing periodic boundary conditions.

Generalized Solution of Inverse Problem for Ising Connection Matrix on d-Dimensional Hypercubic Lattice

“…Finally, in paper [ 10 ], we solved the inverse problem, restoring the interaction constants from the known spectrum of the connection matrix, when was equal to 1, 2, and 3. In the present paper, we generalize these results in the case of the hypercubic lattice of an arbitrary dimension .…”