Spin glass is the simplest disordered system that preserves the full range of complex collective behavior of interacting frustrating elements. In the paper, we propose a novel approach for calculating the values of thermodynamic averages of the frustrated spin glass model using custom deep neural networks. The spin glass system was considered as a specific weighted graph whose spatial distribution of the edges values determines the fundamental characteristics of the system. Special neural network architectures that mimic the structure of spin lattices have been proposed, which has increased the speed of learning and the accuracy of the predictions compared to the basic solution of fully connected neural networks. At the same time, the use of trained neural networks can reduce simulation time by orders of magnitude compared to other classical methods. The validity of the results is confirmed by comparison with numerical simulation with the replica-exchange Monte Carlo method.
We present results of numerical simulation of thermodynamics for array of Classical Heisenberg spins placed on 2D square lattice. By using Metropolis and Wang--Landau methods we show the temperature behaviour of system with competing Heisenberg and Dzyaloshinskii--Moriya interaction (DMI) in contrast with classical Heisenberg system. We show the process of nucleating of skyrmion depending on the value of external magnetic field.
In this paper we present the results of the high-performance computations for the Ising model, the XY-model and the classical Heisenberg model for the pyrochlore lattice. We used Wolff and Swendsen-Wang cluster algorithms with GPU parallelization for the calculations. We obtained critical exponents and critical temperatures using finite-size scaling approach.
We utilize the Metropolis algorithm to obtain statistical averages of the domain wall length in a FePt granular structure after remagnetization is performed by an ultrashort polarized laser impulse. We propose and check the cluster-size-based order parameter, which along with magnetization, shows the domain wall length, and as a consequence, the average cluster size in the system. We treat the inverse Faraday effect as an external directed magnetic field and show impulse time- and laser power- dependent estimates within the Heisenberg model.
Magnetic films, in which magnetic vortex textures - skyrmions appear because of competition between the direct Heisenberg exchange and the Dzyaloshinskii-Moriya interaction, were studied using the Monte-Carlo simulation technique. The conditions for the nucleation and stable existence of magnetic skyrmions in magnetic films in the frame of the classical Heisenberg model were considered in the paper. The process of nucleation of skyrmions with increasing of the external magnetic field was studied, various phases into which the Heisenberg spin system passes were recognized. A phase diagram was plotted: it shows the behavior of the system at the constant value of temperature depending on values of an external magnetic field and Dzyaloshinskii-Moriya interaction.
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