Transactions on Machine Intelligence 2821-1693 8 1 2025 03 01 Phase Transition of the Two-Dimensional Ising Model in a Homogeneous Magnetic Field Using the Metropolis Monte Carlo Algorithm and Separation of Different Phases via CNN 17 25 214198 10.47176/TMI.2025.17 EN R. Rastgar Poor School of Engineering Sciences, College 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 12 03 Quantum spin networks represent configurations of spins arranged on a topological lattice, where the spin interactions are governed by the system's Hamiltonian. These networks are critical for understanding magnetic materials, as the arrangement of spins and the type of interaction between neighboring spins determine the macroscopic behavior of the system. The behavior of these systems is further influenced by the presence of external magnetic fields. In this paper, we first investigate the various phases of the two-dimensional Ising lattice with periodic boundary conditions under the influence of a uniform external magnetic field. The exploration of these phases is performed using the Metropolis Monte Carlo (MP-MN) algorithm, a well-established statistical method for simulating spin systems. Subsequently, we explore the potential of deep learning, specifically convolutional neural networks (CNN), in identifying and predicting these phases of spin lattices. The CNN's ability to classify different phases of the two-dimensional Ising model in the presence of a homogeneous magnetic field at a constant temperature is examined. The study aims to demonstrate how machine learning models, particularly CNNs, can effectively detect phase transitions and predict the system's behavior, which traditionally requires extensive computational methods. Finally, the performance of the CNN algorithm is evaluated by assessing its accuracy in predicting different phases of the Ising model. https://www.tmachineintelligence.ir/article_214198_73b8a31aed7035b0267911340ed25a89.pdf