Machine Learning Phase Transition: An Iterative Methodology

Machine learning provides new techniques to investigate phase transitions in physics. Here, we propose an iterative methodology to find the critical temperature for the two-dimensional Ising model based on machine-learning techniques. Making use of dimension-reduction algorithm, we obtain the incipient phase boundaries and labels for some samples which would be used by a convolutional neural network to find the critical temperature in an iterative manner. During the finding process, the newly labelled samples would be put in the training set and the phase boundaries would be updated toward each other. Meanwhile, the average of the boundaries would converge to the theoretical value. We also compare the relation between the capability of recognition of the convolutional neural network and magnetic susceptibility near the critical point. This work not only offers a methodology to explore unexplored phase transitions for statistical models but also put forward the motivation to study the deep connections between statistical physical models and neural networks.