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Area of Science:

  • Statistical physics
  • Computational physics
  • Machine learning applications

Background:

  • The Berezinskii-Kosterlitz-Thouless (BKT) phase transition is a key phenomenon in 2D systems.
  • Understanding phase transitions is crucial for condensed matter physics.
  • Traditional methods for identifying phase transitions can be computationally intensive.

Purpose of the Study:

  • To develop a novel method for detecting BKT phase transitions.
  • To apply neural network (NN) flow and Jensen-Shannon divergence (JSD) for phase transition analysis.
  • To study the two-dimensional q-state clock model with q≥4.

Main Methods:

  • Utilizing a neural network (NN) flow, comprising sequential variational autoencoder units.
  • Training the NN flow using unsupervised learning on Monte Carlo configurations.
  • Employing Jensen-Shannon divergence (JSD) as an information-distance measure to compare state ensembles.
  • Analyzing the probability distribution functions of mean spin values.

Main Results:

  • The NN flow effectively maps arbitrary spin states to a fixed-point ensemble.
  • The JSD thermometer reveals unique profiles corresponding to different temperatures.
  • These unique JSD profiles accurately identify critical temperatures of BKT phase transitions.
  • The method demonstrates robustness for the 2D q-state clock model (q≥4).

Conclusions:

  • The NN flow method, combined with JSD, provides a powerful tool for identifying BKT phase transitions.
  • This approach offers a data-driven and potentially more efficient alternative to traditional methods.
  • The findings contribute to a deeper understanding of phase transitions in statistical physics models.