Mapping distinct phase transitions to a neural network
Abstract
We demonstrate, by means of a convolutional neural network, that the features learned in the twodimensional Ising model are sufficiently universal to predict the structure of symmetrybreaking phase transitions in considered systems irrespective of the universality class, order, and the presence of discrete or continuous degrees of freedom. No prior knowledge about the existence 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 the critical exponents of the ϕ^{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.
 Publication:

Physical Review E
 Pub Date:
 November 2020
 DOI:
 10.1103/PhysRevE.102.053306
 arXiv:
 arXiv:2007.00355
 Bibcode:
 2020PhRvE.102e3306B
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 doi:10.1103/PhysRevE.102.053306