Machine learning detection of BerezinskiiKosterlitzThouless transitions in q state clock models
Abstract
We demonstrate that a machine learning technique with a simple feedforward neural network can sensitively detect two successive phase transitions associated with the BerezinskiiKosterlitzThouless (BKT) phase in q state clock models simultaneously by analyzing the weight matrix components connecting the hidden and output layers. We find that the method requires only a data set of the raw spatial spin configurations for the learning procedure. This data set is generated by Monte Carlo thermalizations at selected temperatures. Neither prior knowledge of, for example, the transition temperatures, number of phases, and order parameters nor processed data sets of, for example, the vortex configurations, histograms of spin orientations, and correlation functions produced from the original spinconfiguration data are needed, in contrast with most of previously proposed machine learning methods based on supervised learning. Our neural network evaluates the transition temperatures as T_{2}/J =0.921 and T_{1}/J =0.410 for the paramagnetictoBKT transition and BKTtoferromagnetic transition in the eightstate clock model on a square lattice. Both critical temperatures agree well with those evaluated in the previous numerical studies.
 Publication:

Physical Review B
 Pub Date:
 August 2021
 DOI:
 10.1103/PhysRevB.104.075114
 arXiv:
 arXiv:2108.05823
 Bibcode:
 2021PhRvB.104g5114M
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 11pages, 9 figures