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Machine learning for percolation utilizing auxiliary Ising variables.

Junyin Zhang1,2, Bo Zhang1,2, Junyi Xu3

  • 1Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China.

Physical Review. E
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Summary
This summary is machine-generated.

Machine learning accurately identifies phase transitions in percolation systems using a novel auxiliary Ising mapping. This method works across dimensions and transition types, advancing physics applications.

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Area of Science:

  • Statistical physics
  • Condensed matter physics
  • Machine learning applications

Background:

  • Machine learning (ML) is increasingly applied to study phase transitions.
  • Applying ML to percolation systems remains a significant challenge.
  • Existing methods may struggle with diverse system dimensions and transition types.

Purpose of the Study:

  • To develop a novel machine learning approach for studying percolation.
  • To demonstrate the efficacy of the auxiliary Ising mapping method.
  • To explore the classification capabilities of ML for different universality classes.

Main Methods:

  • An auxiliary Ising mapping method was proposed for percolation systems.
  • Unsupervised machine learning was employed to analyze the mapped systems.
  • Neural network machine learning was used for classifying configurations.

Main Results:

  • The proposed method accurately locates the percolation threshold.
  • The accuracy is independent of system spatial dimension and transition type (first-order or continuous).
  • Neural networks achieved high confidence in classifying auxiliary Ising configurations for different universalities.

Conclusions:

  • The auxiliary Ising mapping method simplifies ML application in percolation.
  • This approach enhances ML's utility in statistical and condensed-matter physics.
  • The method shows promise for broader applications in complex physical systems.