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Inverse Problem for Ising Connection Matrix with Long-Range Interaction

Author

Listed:
  • 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)

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.

Suggested Citation

  • Leonid Litinskii & Boris Kryzhanovsky, 2021. "Inverse Problem for Ising Connection Matrix with Long-Range Interaction," Mathematics, MDPI, vol. 9(14), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1624-:d:591505
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    References listed on IDEAS

    as
    1. Litinskii, L.B. & Kryzhanovsky, B.V., 2020. "Eigenvalues of Ising connection matrix with long-range interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    2. Dixon, J.M. & Tuszynski, J.A. & Nip, M.L.A., 2001. "Exact eigenvalues of the Ising Hamiltonian in one-, two- and three-dimensions in the absence of a magnetic field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(1), pages 137-156.
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