Transactions on Machine Intelligence 2821-1693 7 2 2024 03 01 Phase Transition of the 2D Square Ising Model in a Homogeneous Magnetic Field Using the Metropolis Monte Carlo Algorithm and Separation of Different Phases via CNN Method 98 106 191604 10.47176/TMI.2024.98 EN R. Rastgarpour Faculty of Engineering Sciences, School of Engineering, University of Tehran, Tehran, Iran N. Majd Assistant Professor, Department of engineering science, college of engineering, university of Tehran, Tehran, Iran 0000-0002-5652-7405 Journal Article 2024 03 06 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. Quantum Spin Networks Hamiltonian Deep Learning Convolutional Neural Network (CNN) Two-Dimensional Ising Model https://www.tmachineintelligence.ir/article_191604_92c29608543abd49a4b02ccc9469c2fe.pdf