Machine Learning the Phase Transitions of Ising Models with Competing Interactions

The Ising model is fundamental to understanding phase transitions and critical phenomena in statistical physics. While the nearest-neighbor Ising model has been studied using machine learning, incorporating next-nearest neighbor interactions adds complexity to determining its critical temperature [1, 2]. In this study, we use machine learning to estimate the critical temperature of the two-dimensional Ising model with competing nearest and next-nearest neighbor interactions, which introduce new ground states not present in the nearest-neighbor model [3]. We generated extensive spin configuration data through Monte Carlo simulations across a range of temperatures to conduct principal component analysis (PCA) and to train a neural network for phase classification and evaluation of critical behavior. Our results demonstrate that both PCA and the neural network provide accurate predictions of the critical temperature, closely aligning with thermodynamic analysis. This approach highlights the potential of machine learning techniques for exploring critical phenomena in extended Ising models, contributing to the broader application of machine learning in the physical sciences.

[1] J. Carrasquilla and R. G. Melko, Nature Physics 13, 431 (2017).

[2] W. Hu, R. R. P. Singh, and R. T. Scalettar, Physical Review E 95, 062122 (2017).

[3] D. P. Landau, Physical Review B 22, 123 (1980).