Inverse Problem for Ising Connection Matrix with Long-Range Interaction

In the present paper, we examine Ising systems on <i>d</i>-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...

Full description

Bibliographic Details
Main Authors:	Leonid Litinskii, Boris Kryzhanovsky
Format:	Article
Language:	English
Published:	MDPI AG 2021-07-01
Series:	Mathematics
Subjects:	Ising connection matrix long-range interaction eigenvalues inverse problem
Online Access:	https://www.mdpi.com/2227-7390/9/14/1624

id	doaj-af27c69b31524cda9ed7ad408f538828
record_format	Article
spelling	doaj-af27c69b31524cda9ed7ad408f5388282021-07-23T13:52:24ZengMDPI AGMathematics2227-73902021-07-0191624162410.3390/math9141624Inverse Problem for Ising Connection Matrix with Long-Range InteractionLeonid Litinskii0Boris Kryzhanovsky1Center of Optical Neural Technologies, Scientific Research Institute for System Analysis, Russian Academy of Sciences, Nakhimov Ave, 36-1, 117218 Moscow, RussiaCenter of Optical Neural Technologies, Scientific Research Institute for System Analysis, Russian Academy of Sciences, Nakhimov Ave, 36-1, 117218 Moscow, RussiaIn the present paper, we examine Ising systems on <i>d</i>-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.https://www.mdpi.com/2227-7390/9/14/1624Ising connection matrixlong-range interactioneigenvaluesinverse problem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Leonid Litinskii Boris Kryzhanovsky
spellingShingle	Leonid Litinskii Boris Kryzhanovsky Inverse Problem for Ising Connection Matrix with Long-Range Interaction Mathematics Ising connection matrix long-range interaction eigenvalues inverse problem
author_facet	Leonid Litinskii Boris Kryzhanovsky
author_sort	Leonid Litinskii
title	Inverse Problem for Ising Connection Matrix with Long-Range Interaction
title_short	Inverse Problem for Ising Connection Matrix with Long-Range Interaction
title_full	Inverse Problem for Ising Connection Matrix with Long-Range Interaction
title_fullStr	Inverse Problem for Ising Connection Matrix with Long-Range Interaction
title_full_unstemmed	Inverse Problem for Ising Connection Matrix with Long-Range Interaction
title_sort	inverse problem for ising connection matrix with long-range interaction
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2021-07-01
description	In the present paper, we examine Ising systems on <i>d</i>-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.
topic	Ising connection matrix long-range interaction eigenvalues inverse problem
url	https://www.mdpi.com/2227-7390/9/14/1624
work_keys_str_mv	AT leonidlitinskii inverseproblemforisingconnectionmatrixwithlongrangeinteraction AT boriskryzhanovsky inverseproblemforisingconnectionmatrixwithlongrangeinteraction
_version_	1721287261976264704

Inverse Problem for Ising Connection Matrix with Long-Range Interaction

Similar Items