Influence of anisotropy on the study of critical behavior of spin models by machine learning methods

2024. No. 2410.14523.

Sukhoverkhova D., Shchur L.

In this paper, we applied a deep neural network to study the issue of knowledge transferability between statistical mechanics models. The following computer experiment was conducted. A convolutional neural network was trained to solve the problem of binary classification of snapshots of the Ising model's spin configuration on a two-dimensional lattice. During testing, snapshots of the Ising model spins on a lattice with diagonal ferromagnetic and antiferromagnetic connections were fed to the input of the neural network. Estimates of the probability of samples belonging to the paramagnetic phase were obtained from the outputs of the tested network. The analysis of these probabilities allowed us to estimate the critical temperature and the critical correlation length exponent. It turned out that at weak anisotropy the neural network satisfactorily predicts the transition point and the value of the correlation length exponent. Strong anisotropy leads to a noticeable deviation of the predicted values from the precisely known ones. Qualitatively, strong anisotropy is associated with the presence of oscillations of the correlation function above the Stephenson disorder temperature and further approach to the point of the fully frustrated case.

Keywords: машинное обучение, machine learning, анизотропия, корреляционная функция, модель Изинга, correlation function, anisotropy, Ising model, cross-learning, second order phase transition, перекрестное обучение, фазовый переход второго рода