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pro vyhledávání: '"Litinskii, Leonid"'
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:
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:
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
Autor:
Kryzhanovsky, Boris, Litinskii, Leonid
The n-vicinities method for approximate calculations of the partition function of a spin system was proposed previously. The equation of state was obtained in the most general form. In the present publication these results are adapted to the Ising mo
Externí odkaz:
http://arxiv.org/abs/1606.09034
Autor:
Kryzhanovsky, Boris, Litinskii, Leonid
We examined energy spectrums of some particular systems of binary spins. It is shown that the configuration space can be divided into classes, and in the limit the energy distributions in these classes can be approximated by the normal distributions.
Externí odkaz:
http://arxiv.org/abs/1505.03393
Autor:
Kryzhanovsky, Boris, Litinskii, Leonid
The proposed method of the free energy calculation is based on the approximation of the energy distribution in the microcanonical ensemble by the Gaussian distribution. We hope that our approach will be effective for the systems with long-range inter
Externí odkaz:
http://arxiv.org/abs/1410.6696
Publikováno v:
Physical Review E, 2012, Vol.85, No.4
We generalize the standard Hopfield model to the case when a weight is assigned to each input pattern. The weight can be interpreted as the frequency of the pattern occurrence at the input of the network. In the framework of the statistical physics a
Externí odkaz:
http://arxiv.org/abs/1205.0908