Inverse Problem for Ising Connection Matrix with Long-Range Interaction

Mathematics

Leonid Litinskii¹  Boris Kryzhanovsky¹ 

[1] Center of Optical Neural Technologies, Scientific Research Institute for System Analysis, Russian Academy of Sciences, Nakhimov Ave, 36-1, 117218 Moscow, Russia;

关键词: Ising connection matrix;    long-range interaction;    eigenvalues;    inverse problem;   

DOI  :  10.3390/math9141624

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown