Machine Learning of the Two-Dimensional Diluted Bond Ising Model

The bond-diluted 2D Ising model is essential for understanding the effects of disorder on magnetic systems. Although the T-p phase diagram of this model has been developed through analytical methods and Monte Carlo simulations, the region near the percolation threshold pc remains insufficiently explored. In this study, we reinvestigate the impact of bond dilution on phase transitions in the bond-diluted 2D Ising model using a machine learning approach. A convolutional neural network, initially trained on data from the pure (undiluted) 2D Ising model, is employed through transfer learning to analyze bond-diluted systems. The numerical results show that as bond concentration decreases, the critical temperature also decreases, in agreement with previous Monte Carlo simulation results. Moreover, these findings are instrumental in estimating the critical bond dilution near the percolation threshold pc. As a result, a comprehensive phase diagram for the bond-diluted 2D Ising model has been constructed.