Using learning by confusion to identify the order of a phase transition*

The conventional methods of classification of phase transitions rely on identification of order parameters and singularities in the free energy and its derivatives. Recently, artificial neural networks have been proven to be an efficient tool to perform this task. It has been shown that properly trained neural networks can precisely determine the critical temperature. One of the approaches is based on "learning by confusion", which is a combination of supervised and unsupervised learning. We show that the degree of neural network's "confusion" can be used to determine the order of the phase transition. For a few selected models we demonstrate how this method can be used to distinguish between first and second order phase transitions.