Влияние анизотропии на исследование критического поведения спиновых моделей методами машинного обучения

Письма в Журнал экспериментальной и теоретической физики. 2024. Т. 120. № 8. С. 644–649.

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 snapshots of the location of spins of the Ising model 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 probabilities 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 index. It turned out that at weak anisotropy the neural network satisfactorily predicts the transition point and the value of the correlation length index. 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 Stefenson disorder onset temperature and further approach to the point of the fully frustrated case.

Keywords: машинное обучение, анизотропия, модель Изинга, phase transition, anisotropy, transfer learning, перенос обучения, фазовый переход, Ising model, Machine learning