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Monte Carlo simulations for D = 1, B = 0.9. Top panel: specific heat, magnetization and chirality as a function of temperature. Bottom panel: three snapshots and their corresponding Sq for three different temperatures, indicated as vertical lines in the plots from the top panel. At the lowest simulated temperature, the system is in the ferromagnetic phase, but an intermediate skyrmion gas phase is clearly seen at higher T .
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Recently, there has been an increased interest in the application of machine learning (ML) techniques to a variety of problems in condensed matter physics. In this regard, of particular significance
is the characterization of simple and complex phases of matter. Here, we use a ML approach to construct the full phase diagram of a well known spin mod...
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... their respective S q at different temperatures. In Fig. 2, at B = 0.2, we see that, at low temperature, the system is in a Sp phase, with the typical single-q S q . At higher T , there is nonzero chirality and the snapshots show a Bm phase, which goes from single-q to a less defined S q . A similar behavior is seen at higher fields (B = 0.9) in Fig. 3, but comparing here a ferromagnetic phase at low temperature with an intermediate skyrmion gas phase. In the higher-temperature snapshot, which corresponds to the highest value of the chirality, we can also see that although the system has a net chirality, thermal fluctuations break the skyrmion and less-defined chiral structures are ...
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... account the intermediate phases. On one hand, the system does not present a clear transition between phases with temperature. On the other hand, specially at higher temperatures, these configurations do not have a characteristic structure factor. We illustrate this showing the results of Monte Carlo simulations for D = 1 in Fig. 2 (B = 0.2) and Fig. 3 (B = 0.9). In both cases, we plot the resulting specific heat, and chirality as a function of temperature, and show three different snapshots and their respective S q at different temperatures. In Fig. 2, at B = 0.2, we see that at low temperature the system is in a Sp phase, with the typical single-q S q . At higher T , there is ...
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... their respective S q at different temperatures. In Fig. 2, at B = 0.2, we see that at low temperature the system is in a Sp phase, with the typical single-q S q . At higher T , there is non-zero chirality and the snapshots show a Bm phase, which goes from single-q to a less defined S q . A similar behavior is seen at higher fields (B = 0.9) in Fig. 3, but comparing here a ferromagnetic phase at low temperature and an intermediate skyrmion gas phase. In the higher temperature snapshot, which corresponds to the highest value of the chirality, we can also see that although the system has a net chirality, thermal fluctuations break the skyrmion and less-defined chiral structures are ...
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We present an in-depth study of the competition between skyrmions and a chiral spin liquid in a model on the kagome lattice that was recently proposed by some of the authors [H. D. Rosales, et al. Phys. Rev. Lett. 130, 106703 (2023)]. We present an analytical overview of the low-energy states using the Luttinger-Tisza approximation. Then we add the...
Citations
... Later, more complicated convolutional neural networks (CNN) were used to study the effect of uniaxial magneto- crystalline anisotropy pointing in the z direction on the phase diagram of a disk-shaped system, 54) and to construct detailed phase diagrams for skyrmion systems including intermediate regions and paramagnetic state. 55) Moreover, it was shown that such an architecture is able to not only determine phase boundaries but also restore various parameters. The authors of Ref. 56 have demonstrated, that a CNN trained on ground state configurations successfully recovers the chirality and magnetization of a given spin texture, as well as the temperature and external magnetic field at which it was stabilized. ...
... Of particular interest is the classification of different phases and the identification of phase transitions of many-body systems [17][18][19][20][21][22][23][24][25][26]. For example, deep neural networks (NN) have been employed to distinguish the ordered or critical phases from the high-temperature disordered state in various classical spin systems [17,[27][28][29][30][31][32]. With proper feature engineering, ML models have also been developed to capture topologically nontrivial phases or many-body localized states [33][34][35][36][37]. ...
... Since each node of the input layer corresponds to an Ising spin of the 2D lattice, the size of the input layer depends on the system size. Similar ML approaches have since been developed for phase classification of numerous classical many-body systems [27][28][29][30][31][32]. However, the architecture of such ML models obviously lacks scalability: ML model developed for a particular system size cannot be directly applied to systems of larger dimensions. ...
We present a scalable machine learning (ML) framework for predicting intensive properties and particularly classifying phases of many-body systems. Scalability and transferability are central to the unprecedented computational efficiency of ML methods. In general, linear-scaling computation can be achieved through the divide and conquer approach, and the locality of physical properties is key to partitioning the system into sub-domains that can be solved separately. Based on the locality assumption, ML model is developed for the prediction of intensive properties of a finite-size block. Predictions of large-scale systems can then be obtained by averaging results of the ML model from randomly sampled blocks of the system. We show that the applicability of this approach depends on whether the block-size of the ML model is greater than the characteristic length scale of the system. In particular, in the case of phase identification across a critical point, the accuracy of the ML prediction is limited by the diverging correlation length. The two-dimensional Ising model is used to demonstrate the proposed framework. We obtain an intriguing scaling relation between the prediction accuracy and the ratio of ML block size over the spin-spin correlation length. Implications for practical applications are also discussed.
... As long as they are adequately selected, machine learning models can be trained with a relatively small set of samples and then used to analyze any new data generated through simulations automatically. In particular, Convolutional Neural Networks (CNNs) have been successfully applied to this type of task: to identify the phase [27][28][29][30][31][32], the topological charge [33] or the DM interaction [34] from 2D images of a spin-lattice; and to find the phase from videos of the lattice [35]. ...
Chiral magnets have attracted a large amount of research interest in recent years because they support a variety of topological defects, such as skyrmions and bimerons, and allow for their observation and manipulation through several techniques. They also have a wide range of applications in the field of spintronics, particularly in developing new technologies for memory storage devices. However, the vast amount of data generated in these experimental and theoretical studies requires adequate tools, among which machine learning is crucial. We use a Convolutional Neural Network (CNN) to identify the relevant features in the thermodynamical phases of chiral magnets, including (anti-)skyrmions, bimerons, and helical and ferromagnetic states. We use a flexible multi-label classification framework that can correctly classify states in which different features and phases are mixed. We then train the CNN to predict the features of the final state from snapshots of intermediate states of a lattice Monte Carlo simulation. The trained model allows identifying the different phases reliably and early in the formation process. Thus, the CNN can significantly speed up the large-scale simulations for 3D materials that have been the bottleneck for quantitative studies so far. Moreover, this approach can be applied to the identification of mixed states and emerging features in real-world images of chiral magnets.
Classifying skyrmionic textures and extracting magnetic Hamiltonian parameters represent crucial and challenging pursuits within the realm of two-dimensional (2D) spintronics. In this study, we leverage micromagnetic simulation and machine learning (ML) to theoretically achieve the recognition of nine distinct skyrmionic textures and the extraction of magnetic Hamiltonian parameters from extensive spin texture images in a 2D Heisenberg model. For texture classification, a deep neural network (DNN) trained through transfer learning is proposed to enable the accurate discrimination of nine diverse skyrmionic textures. In parallel, for parameter extraction, based on the textures generated by different Heisenberg exchange stiffnesses (J), Dzyaloshinskii-Moriya strengths (D), and anisotropy constants (K), we employ a multi-input single-output (MISO) deep learning model (handling both images and parameters) and a support vector regression (SVR) model (dealing with Fourier features) to extract the parameters embedded in the spin textures. Our models for classification and extraction demonstrate significant success, achieving an accuracy of 98% (DNN), and R-squared (R2) of 0.90 (MISO) and 0.8 (SVR). Notably, our ML methods prove their effectiveness in distinguishing skyrmionic textures with blurred phase boundaries, thereby contributing to a more nuanced understanding of these textures. Additionally, our models establish a mapping relationship between spin texture images and magnetic parameters, thus validating the feasibility of extracting microscopic mechanisms from experimental images. This finding offers significant guidance for spintronics experiments, emphasizing the potential of ML methods in elucidating intricate details from practical observations.
We present a scalable machine learning (ML) framework for predicting intensive properties and particularly classifying phases of Ising models. Scalability and transferability are central to the unprecedented computational efficiency of ML methods. In general, linear-scaling computation can be achieved through the divide-and-conquer approach, and the locality of physical properties is key to partitioning the system into subdomains that can be solved separately. Based on the locality assumption, ML model is developed for the prediction of intensive properties of a finite-size block. Predictions of large-scale systems can then be obtained by averaging results of the ML model from randomly sampled blocks of the system. We show that the applicability of this approach depends on whether the block-size of the ML model is greater than the characteristic length scale of the system. In particular, in the case of phase identification across a critical point, the accuracy of the ML prediction is limited by the diverging correlation length. We obtain an intriguing scaling relation between the prediction accuracy and the ratio of ML block size over the spin-spin correlation length. Implications for practical applications are also discussed. While the two-dimensional Ising model is used to demonstrate the proposed approach, the ML framework can be generalized to other many-body or condensed-matter systems.
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