Inverse Problem for Ising Connection Matrix with Long-Range Interaction

Leonid Litinskii and Boris Kryzhanovsky
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Leonid Litinskii: Center of Optical Neural Technologies, Scientific Research Institute for System Analysis, Russian Academy of Sciences, Nakhimov Ave, 36-1, 117218 Moscow, Russia
Boris Kryzhanovsky: Center of Optical Neural Technologies, Scientific Research Institute for System Analysis, Russian Academy of Sciences, Nakhimov Ave, 36-1, 117218 Moscow, Russia

Mathematics, 2021, vol. 9, issue 14, 1-11

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.

Keywords: Ising connection matrix; long-range interaction; eigenvalues; inverse problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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