The area of Machine learning (ML) has seen exceptional growth in recent years. Successful implementation of ML methods in various branches of physics has led to new insights. These methods have been shown to classify phases in condensed matter systems. Here we study the classification problem of phases in a system of hard rigid rods on a square lattice around a continuous and a discontinuous phase transition. On comparing a number of methods we find that convolutional neural network (CNN) classifies the phases with the highest accuracy when only snapshots are given as inputs. We study how the system size affects the model performance. We further compare the performance of CNN in classifying the phases around a continuous and a discontinuous phase transition. Further, we show that one can even beat the accuracy of CNN with simpler models by using physics-guided features. Lastly, we show that the critical point in this system can be learned without any prior estimate by using only the information of the ordered phase (as training set). Our study reveals the ML techniques that have been successful in studying spin systems can be easily adapted to more complex systems.
The area of Machine learning (ML) has seen exceptional growth in recent years. Successful implementation of ML methods in various branches of physics has led to new insights. These methods have been shown to classify phases in condensed matter systems. Here we study the classification problem of phases in a system of hard rigid rods on a square lattice around a continuous and a discontinuous phase transition. On comparing a number of methods we find that convolutional neural network (CNN) classifies the phases with the highest accuracy when only snapshots are given as inputs. We study how the system size affects the model performance. We further compare the performance of CNN in classifying the phases around a continuous and a discontinuous phase transition. Further, we show that one can even beat the accuracy of CNN with simpler models by using physics-guided features. Lastly, we show that the critical point in this system can be learned without any prior estimate by using only the information of the ordered phase (as training set). Our study reveals the ML techniques that have been successful in studying spin systems can be easily adapted to more complex systems.
Machine learning algorithms provide a new perspective on the study of physical phenomena. In this Rapid Communication, we explore the nature of quantum phase transitions using a multicolor convolutional neural network (CNN) in combination with quantum Monte Carlo simulations. We propose a method that compresses (d+1)-dimensional space-time configurations to a manageable size and then use them as the input for a CNN. We benchmark our approach on two models and show that both continuous and discontinuous quantum phase transitions can be well detected and characterized. Moreover, we show that intermediate phases, which were not trained, can also be identified using our approach.
Computational models adequately representing phase transitions and evaluating the critical system parameters are essential for the understanding of the properties of a wide range of materials. Here we propose a machine learning (ML)-based approach to the identification of the critical point in anisotropic spin systems. Our approach implies training of a convolutional neural network (CNN) model from the correlation matrices obtained by Monte Carlo simulations. Next, the pretrained model is employed as a fast estimator of the critical temperature, which can be extracted in several complementary ways from the CNN model inference, this way improving the robustness of the analysis. The ML-based estimates obtained in this study are in very good agreement with the reference Monte Carlo simulation results, while computational costs are about 10x lower compared to the classical thermodynamic approach.
The identification and characterization of phase transitions is one of the oldest and most central problems in condensed matter physics, traditionally approached through order parameters, free-energy expansions, renormalization-group analysis, and direct numerical simulation. Over the past decade, machine learning (ML) has emerged as a complementary and, in some regimes, transformative methodology for this task. Supervised classifiers can learn to distinguish phases directly from raw configurations without an a priori order parameter; unsupervised and self-supervised techniques such as principal component analysis, autoencoders, and learning-by-confusion can locate transition points with minimal or no labeled data; and generative and variational architectures, including neural-network quantum states, now approximate ground-state wavefunctions of strongly correlated systems well beyond the reach of exact diagonalization. This paper reviews the theoretical foundations of phase transitions relevant to machine-learning applications, surveys the principal families of algorithms used to detect and classify phases, and examines their application across classical spin systems, percolation, topological and quantum phases, strongly correlated electron systems, and experimentally measured spectroscopic data. Representative case studies are discussed, including convolutional and graph-neural-network classifiers of lattice configurations, explainable-ML detection of thermodynamic transitions in photoemission spectra, and deep-learning-guided discovery of high-temperature superconductors. The review closes with a critical discussion of persistent challenges interpretability, data scarcity in correlated-electron experiments, generalization across Hamiltonians, and the reliability of learned order parameters near criticality and outlines directions for future research, including physics-informed architectures, uncertainty quantification, and closed-loop integration with autonomous experimentation.
We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were previously found to be efficient in classifying phases and locating phase transitions of various basic model systems. In order to rationalize the emergence of the classification process and for identifying any underlying physical quantities, it is feasible to examine the weight matrices and the convolutional filter kernels that result from the learning process of such shallow networks. Furthermore, we demonstrate how the learning-by-confusing scheme can be used, in combination with a simple threshold-value classification method, to diagnose the learning parameters of neural networks. In particular, we study the classification process of both fully-connected and convolutional neural networks for the two-dimensional Ising model with extended domain wall configurations included in the low-temperature regime. Moreover, we consider the two-dimensional XY model and contrast the performance of the learning-by-confusing scheme and convolutional neural networks trained on bare spin configurations to the case of preprocessed samples with respect to vortex configurations. We discuss these findings in relation to similar recent investigations and possible further applications.
This paper presents the investigation of convolutional neural network (CNN) prediction successfully recognizing the temperature of the nonequilibrium phase transitions in two-dimensional (2D) Ising spins on a square lattice. The model uses image snapshots of ferromagnetic 2D spin configurations as an input shape to provide the average output predictions. By considering supervised machine learning techniques, we perform Metropolis Monte Carlo (MC) simulations to generate the configurations. In the equilibrium Ising model, the Metropolis algorithm respects detailed balance condition (DBC), while its nonequilibrium version violates DBC. Violating the DBC of the algorithm is characterized by a parameter −8<ε<8. We find the exact result of the transition temperature Tc(ε) in terms of ε. If we set ε=0, the usual single spin-flip algorithm can be restored, and the equilibrium configurations generated with such a set up are used to train our model. For ε≠0, the system attains the nonequilibrium steady states (NESS), and the modified algorithm generates NESS configurations (test dataset). The trained model is successfully tested on the test dataset. Our result shows that CNN can determine Tc(ε≠0) for various ε values, consistent with the exact result.
Quantum spin networks represent systems in which quantum spins are arranged on a topological lattice, where the nature of spin interactions and the influence of external magnetic fields can lead to complex collective behaviors. The Hamiltonian governing such systems determines the energy landscape and phase transitions under various thermodynamic conditions. In this paper, we focus on the two-dimensional Ising spin model with periodic boundary conditions subjected to a uniform external magnetic field. Initially, we employ the Metropolis Monte Carlo (MP-MN) algorithm to simulate the system and identify its phase transitions at different magnetic field strengths. The emergence of ordered and disordered phases in response to thermal fluctuations and magnetic interactions is systematically analyzed. Subsequently, we explore the application of convolutional neural networks (CNNs), a powerful class of deep learning models, to detect and classify the phases of the Ising model based on spin configurations generated at a fixed temperature. The CNN is trained using labeled data representing different magnetic field values, and its performance in phase prediction is quantitatively evaluated. The results demonstrate that CNNs can successfully learn complex spin patterns and provide accurate classification of spin phases, highlighting their potential for analyzing phase transitions in statistical physics models.