A Mapping of Distinct Phase Transitions to a Neural Network

We demonstrate, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of phase transitions in systems irrespective of the universality class, order, and discrete or continuous degrees of freedom. No prior knowledge about the presence of a phase transition is required in the target system and its entire parameter space can be scanned with multiple histogram reweighting to discover one. We establish our approach in q-state Potts models and perform a calculation for the critical coupling and critical exponents of the $\phi^{4}$ scalar field theory using quantities derived from the neural network implementation. We view the machine learning algorithm as a mapping that associates each configuration across different systems to its corresponding phase and elaborate on implications for the discovery of unknown phase transitions.