Using Convolutional Neural Networks to analyze phase transitions and calculate critical exponents

Identifying phase transitions and their corresponding order parameters is a central problem in physics, but estimation of order parameters from experimental measurements is difficult. In this work, we present an alternative framework for analyzing phase transitions by using neural networks to learn order parameters directly from data. By introducing a type of convolutional architecture, we show how these methods can be made more robust by systematically increasing the convolutional window size. We investigate the extraction of correlation length critical exponents by performing finite-size scaling on the network, and use this to analyze the 1D TFIM phase transition from measurements in different bases. This work is a step towards a machine learning toolkit for characterizing phase transitions without prior knowledge.