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Register a new userPhase diagram study of a two-dimensional frustrated antiferromagnet via unsupervised machine learning
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Added by
Carlos Alberto Lamas
Publication date
2021
fields
Physics
and research's language is
English
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We apply unsupervised learning techniques to classify the different phases of the $J_1-J_2$ antiferromagnetic Ising model on the honeycomb lattice. We construct the phase diagram of the system using convolutional autoencoders. These neural networks can detect phase transitions in the system via `anomaly detection, without the need for any label or a priori knowledge of the phases. We present different ways of training these autoencoders and we evaluate them to discriminate between distinct magnetic phases. In this process, we highlight the case of high temperature or even random training data. Finally, we analyze the capability of the autoencoder to detect the ground state degeneracy through the reconstruction error.
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We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop like transition in the considered isotropic spin model.
Three-dimensional (3D) antiferromagnets with random magnetic anisotropy (RMA) experimentally studied to date do not have random single-ion anisotropies, but rather have competing two-dimensional and three-dimensional exchange interactions which can obscure the authentic effects of RMA. The magnetic phase diagram Fe$_{x}$Ni$_{1-x}$F$_{2}$ epitaxial thin films with true random single-ion anisotropy was deduced from magnetometry and neutron scattering measurements and analyzed using mean field theory. Regions with uniaxial, oblique and easy plane anisotropies were identified. A RMA-induced glass region was discovered where a Griffiths-like breakdown of long-range spin order occurs.
We report magnetization and specific heat measurements in the 2D frustrated spin-1/2 Heisenberg antiferromagnet Cs2CuCl4 at temperatures down to 0.05 K and high magnetic fields up to 11.5 T applied along a, b and c-axes. The low-field susceptibility chi (T) M/B shows a broad maximum around 2.8 K characteristic of short-range antiferromagnetic correlations and the overall temperature dependence is well described by high temperature series expansion calculations for the partially frustrated triangular lattice with J=4.46 K and J/J=1/3. At much lower temperatures (< 0.4 K) and in in-plane field (along b and c-axes) several new intermediate-field ordered phases are observed in-between the low-field incommensurate spiral and the high-field saturated ferromagnetic state. The ground state energy extracted from the magnetization curve shows strong zero-point quantum fluctuations in the ground state at low and intermediate fields.
The classification of phase transitions is a central and challenging task in condensed matter physics. Typically, it relies on the identification of order parameters and the analysis of singularities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions, employing both unsupervised and supervised machine learning techniques. Using the axial next-nearest neighbor Ising (ANNNI) model as a benchmark, we show how unsupervised learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase) as well as two distinct regions within the paramagnetic phase. Employing supervised learning we show that transfer learning becomes possible: a machine trained only with nearest-neighbour interactions can learn to identify a new type of phase occurring when next-nearest-neighbour interactions are introduced. All our results rely on few and low dimensional input data (up to twelve lattice sites), thus providing a computational friendly and general framework for the study of phase transitions in many-body systems.
Using the dynamical mean-field approximation we investigate formation of excitonic condensate in the two-band Hubbard model in the vicinity of the spin-state transition. With temperature and band filling as the control parameters we realize all symmetry allowed spin-triplet excitonic phases, some exhibiting a ferromagnetic polarization. While the transitions are first-order at low temperatures, at elevated temperatures continuous transitions are found that give rise to a multi-critical point. Rapid but continuous transition between ferromagnetic and non-magnetic excitonic phases allows switching of uniform magnetization by small changes of chemical potential.
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