Zobrazeno 1 - 10
of 406
pro vyhledávání: '"Litinskii, A."'
We use an m-vicinity method to examine Ising models on hypercube lattices of high dimensions d>=3. This method is applicable for both short-range and long-range interactions. We introduce a small parameter, which determines whether the method can be
Externí odkaz:
http://arxiv.org/abs/2105.14460
The previously developed n-vicinity method allows us to calculate accurately critical values of inverse temperatures for Ising models with short-range interaction. We generalize the method to the case of long-range interactions in spin systems and ob
Externí odkaz:
http://arxiv.org/abs/2012.06787
Autor:
Litinskii, Leonid, Kryzhanovsky, Boris
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 it eigenvalues. In addition, we
Externí odkaz:
http://arxiv.org/abs/2012.06778
Autor:
Kryzhanovsky, B. V., Litinskii, L. B.
We examine connection matrices of Ising systems with long-rang interaction on d-dimensional hypercube lattices of linear dimensions L. We express the eigenvectors of these matrices as the Kronecker products of the eigenvectors for the one-dimensional
Externí odkaz:
http://arxiv.org/abs/2008.04227
Autor:
Litinskii, L. B., Kaganowa, I. M.
Publikováno v:
In: Kryzhanovsky B. et al. (eds) Advances in Neural Computation, Machine Learning, and Cognitive Research III. Studies in Computational Intelligence (2020) vol 856, pp.412-419. Springer, Cham
We give an account of the Axelrod-Bennet model that describes formation of a bimodal coalition. We present its initial formalism and applications and reformulate the problem in terms of the Hopfield model. This allowed us to analyze a system of two h
Externí odkaz:
http://arxiv.org/abs/2001.09716
Autor:
Litinskii, Leonid, Kryzhanovsky, Boris
We obtained analytically eigenvalues of a multidimensional Ising Hamiltonian on a hypercube lattice and expressed them in terms of spin-spin interaction constants and the eigenvalues of the one-dimensional Ising Hamiltonian (the latter are well known
Externí odkaz:
http://arxiv.org/abs/2001.09692
Autor:
Kryzhanovsky, B. V., Litinskii, L. B.
For a 1D Ising model, we obtained an exact expression for the spectral density in an n-vicinity of the ground state and explained why our n-vicinity method with the Gaussian approximation of the spectral density did not applicable in this case. We al
Externí odkaz:
http://arxiv.org/abs/1811.08703
Autor:
Litinskii, Leonid, Kryzhanovsky, Boris
For planar and cubic Ising models, we examined two ways of approximation of a spectral density that describes a degeneracy of energy levels. We approximated the exponent of the spectral density by polynomials of even degrees and using our n-vicinity
Externí odkaz:
http://arxiv.org/abs/1804.03996
Autor:
Kryzhanovsky, Boris, Litinskii, Leonid
In a previous work, the n-vicinity method for approximate calculation of the partition function of a spin system was proposed. The equation of state was obtained in the most general form. In the present paper, we analyze the applicability of this met
Externí odkaz:
http://arxiv.org/abs/1701.07332
Publikováno v:
Entropy, Vol 25, Iss 10, p 1428 (2023)
In the framework of mean field approximation, we consider a spin system consisting of two interacting sub-ensembles. The intra-ensemble interactions are ferromagnetic, while the inter-ensemble interactions are antiferromagnetic. We define the effecti
Externí odkaz:
https://doaj.org/article/f6d16b09e2d242c7860b4cb5be5de362
