Machine learning phase transition: An iterative proposal
Abstract
We propose an iterative proposal to estimate critical points for statistical models based on configurations by combining machinelearning tools. Firstly, phase scenarios and preliminary boundaries of phases are obtained by dimensionalityreduction techniques. Besides, this step not only provides labeled samples for the subsequent step but also is necessary for its application to novel statistical models. Secondly, making use of these samples as training set, neural networks would be employed to assign labels to those samples between the phase boundaries in an iterative manner. Newly labeled samples would be put in the training set used in subsequent training and the phase boundaries would be updated as well. The average of the phase boundaries is expected to converge to the critical temperature in this proposal. In concrete examples, we implement this proposal to estimate the critical temperatures for two qstate Potts models with continuous and first order phase transitions. Techniques used in linear and manifold dimensionalityreductions are employed in the first step. Both a convolutional neural network and a bidirectional recurrent neural network with long shortterm memory units perform well for two Potts models in the second step. The convergent behaviors of the estimations reflect the types of phase transitions. And the results indicate that our proposal may be used to explore phase transitions for new general statistical models.
 Publication:

Annals of Physics
 Pub Date:
 November 2019
 DOI:
 10.1016/j.aop.2019.167938
 arXiv:
 arXiv:1808.01731
 Bibcode:
 2019AnPhy.41067938Z
 Keywords:

 Machine learning;
 Neural network;
 Phase transition;
 Condensed Matter  Disordered Systems and Neural Networks;
 Physics  Computational Physics
 EPrint:
 We focus on the iterative strategy but not the concrete tools like specific dimensionreduction techniques, CNN and BLSTM in this work. Other machinelearning tools with similar functions may be applied to new statistical models with this proposal