Generalized Solution of Inverse Problem for Ising Connection Matrix on <i>d</i>-Dimensional Hypercubic Lattice
We analyze a connection matrix of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>d</mi></semantics></math></inline-formula>-dimensional Ising system and solve the inverse problem,...
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MDPI AG
2022-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/10/1424 |
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| author | Boris Kryzhanovsky Leonid Litinskii |
| author_facet | Boris Kryzhanovsky Leonid Litinskii |
| author_sort | Boris Kryzhanovsky |
| collection | DOAJ |
| description | We analyze a connection matrix of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>d</mi></semantics></math></inline-formula>-dimensional Ising system and solve the inverse problem, restoring the constants of interaction between spins, based on the known spectrum of its eigenvalues. When the boundary conditions are periodic, we can account for interactions between spins that are arbitrarily far. In the case of the free boundary conditions, we have to restrict ourselves with interactions between the given spin and the spins of the first <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>d</mi></semantics></math></inline-formula> coordination spheres. |
| first_indexed | 2024-03-09T20:14:51Z |
| format | Article |
| id | doaj.art-b566923a74c84a1185e9b4d8f7b8056a |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T20:14:51Z |
| publishDate | 2022-10-01 |
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| series | Entropy |
| spelling | doaj.art-b566923a74c84a1185e9b4d8f7b8056a2023-11-24T00:03:31ZengMDPI AGEntropy1099-43002022-10-012410142410.3390/e24101424Generalized Solution of Inverse Problem for Ising Connection Matrix on <i>d</i>-Dimensional Hypercubic LatticeBoris Kryzhanovsky0Leonid Litinskii1Center 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, RussiaWe analyze a connection matrix of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>d</mi></semantics></math></inline-formula>-dimensional Ising system and solve the inverse problem, restoring the constants of interaction between spins, based on the known spectrum of its eigenvalues. When the boundary conditions are periodic, we can account for interactions between spins that are arbitrarily far. In the case of the free boundary conditions, we have to restrict ourselves with interactions between the given spin and the spins of the first <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>d</mi></semantics></math></inline-formula> coordination spheres.https://www.mdpi.com/1099-4300/24/10/1424Ising connection matrixeigenvaluesKronecker productinverse problem |
| spellingShingle | Boris Kryzhanovsky Leonid Litinskii Generalized Solution of Inverse Problem for Ising Connection Matrix on <i>d</i>-Dimensional Hypercubic Lattice Entropy Ising connection matrix eigenvalues Kronecker product inverse problem |
| title | Generalized Solution of Inverse Problem for Ising Connection Matrix on <i>d</i>-Dimensional Hypercubic Lattice |
| title_full | Generalized Solution of Inverse Problem for Ising Connection Matrix on <i>d</i>-Dimensional Hypercubic Lattice |
| title_fullStr | Generalized Solution of Inverse Problem for Ising Connection Matrix on <i>d</i>-Dimensional Hypercubic Lattice |
| title_full_unstemmed | Generalized Solution of Inverse Problem for Ising Connection Matrix on <i>d</i>-Dimensional Hypercubic Lattice |
| title_short | Generalized Solution of Inverse Problem for Ising Connection Matrix on <i>d</i>-Dimensional Hypercubic Lattice |
| title_sort | generalized solution of inverse problem for ising connection matrix on i d i dimensional hypercubic lattice |
| topic | Ising connection matrix eigenvalues Kronecker product inverse problem |
| url | https://www.mdpi.com/1099-4300/24/10/1424 |
| work_keys_str_mv | AT boriskryzhanovsky generalizedsolutionofinverseproblemforisingconnectionmatrixonididimensionalhypercubiclattice AT leonidlitinskii generalizedsolutionofinverseproblemforisingconnectionmatrixonididimensionalhypercubiclattice |