Phases and Phase Transitions in Hexagonal Ising Lattices Identified by Machine Learning

Hugo Yánez-Rueda, Dayanara Yánez-Arcos

Vasanth Kumar Babu, Rahul Anil Pandit

Akimichi Sakamoto, Kenta Shiina, 弘之 森

A new idea of preparing data is proposed for application of machine-learning methods to analysis of phase transitions of Ising model. Presenting spin configurations with different sizes in single-size images, we could test the different-size spin configurations by using a neural network trained with spin configurations with a fixed size. We also analyzed the Ising model on triangular and hexagonal lattices using the neural network trained for square lattice.

Eugenio Emilio Vogel, Bernardo Fierro, F. Bachmann

Askery Canabarro, F. F. Fanchini, André Luiz Malvezzi +2 more

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-neighbor interactions can learn to identify a new type of phase occurring when next-nearest-neighbor 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.

Rui Zhang, Bin Wei, Dong Zhang +2 more

We investigate theoretically the phase transition in a three-dimensional cubic Ising model utilizing state-of-the-art machine learning algorithms. Supervised machine learning models show high accuracies (99%) in phase classification and very small relative errors ($<{10}^{\ensuremath{-}4}$) of the energies in different spin configurations. Unsupervised machine learning models are introduced to study the spin configuration reconstructions and reductions, and the phases of reconstructed spin configurations can be accurately classified by a linear logistic algorithm. Based on the comparison between various machine learning models, we develop a few-shot strategy to predict phase transitions in larger lattices from a trained sample in smaller lattices. The few-shot machine learning strategy for a three-dimensional (3D) Ising model enables us to study the 3D Ising model efficiently and provides an integrated and highly accurate approach to other spin models.