Mapping distinct phase transitions to a neural network

TL;DR

This paper shows that a convolutional neural network trained on the 2D Ising model can universally identify and analyze phase transitions across various systems without prior knowledge, including critical points and exponents.

Contribution

The study introduces a neural network approach that generalizes learned features from the Ising model to predict phase transition structures in diverse systems, regardless of their universality class or degrees of freedom.

Findings

Successfully predicts phase transition structures in different models.

Determines critical coupling and exponents for scalar field theory.

Identifies phase boundaries without prior system-specific knowledge.

Abstract

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 symmetry-breaking 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 $\phi^{4}$ 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.