arXiv subjects

Magomed Malsagov

Publications and source records attributed to Magomed Malsagov.

3 recordsLinked to original sources

arXiv2020

Investigation of Finite-size 2D Ising Model with a Noisy Matrix of Spin-Spin Interactions

We analyze changes in the thermodynamic properties of a spin system when it passes from the classical two-dimensional Ising model to the spin glass model, where spin-spin interactions are random in their values and signs. Formally, the transition reduces to a gradual change in the amplitude of the multiplicative noise (distributed uniformly with a mean equal to one) superimposed over the initial Ising matrix of interacting spins. Considering the noise, we obtain analytical expressions that are valid for lattices of finite sizes. We compare our results with the results of computer simulations performed for square $N=L{\times}L$ lattices with linear dimensions $L = 50÷1000$. We find experimentally the dependencies of the critical values (the critical temperature, the internal energy, entropy and the specific heat) as well as the dependencies of the energy of the ground state and its magnetization on the amplitude of the noise. We show that when the variance of the noise reaches one, there is a jump of the ground state from the fully correlated state to an uncorrelated state and its magnetization jumps from 1 to 0. In the same time, a phase transition that is present at a lower level of the noise disappears.

cond-mat.dis-nn↗

arXiv2016

The Spectra of Local Minima in Spin-Glass Models

The spectra of spin models have been investigated in computation experiments. For the Sherrington-Kirkpatrick and Edwards-Anderson models we have determined the basic spectral characteristics: the average depth of a local minimum, the spectrum width, the depth of the global minimum. The experimental data are used to build the relations between these quantities and the model dimensionality N and find their asymptotic values for N goes to infinity.

cond-mat.dis-nn↗

arXiv2012

Discretization of a matrix in the problem of quadratic functional binary minimization

The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that optimal procedure of replacement matrix elements by the integer quantities with the limited number of gradations exist, and the efficient of minimization does not reduce. Parameter depends on matrix properties, which allows estimate the capability of using described procedure for given type of matrix, is found. Computational complexities of algorithm and RAM requirements are reduced by 16 times, correct using of integer elements allows increase minimization algorithm speed by the orders.

cs.NE↗