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Inverse problem beyond two-body interaction: The cubic mean-field Ising model.

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We successfully reconstructed free parameters for the cubic mean-field Ising model using configuration data. This method proved robust across unique and multiple thermodynamic phase regions.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics

Background:

  • The cubic mean-field Ising model is a fundamental model in statistical mechanics.
  • Solving the inverse problem is crucial for understanding model parameters from observed data.

Purpose of the Study:

  • To develop and validate a method for reconstructing free parameters of the cubic mean-field Ising model.
  • To assess the robustness of the inversion technique.

Main Methods:

  • Utilizing configuration data generated from the model's distribution.
  • Applying an inverse problem-solving procedure to reconstruct system parameters.

Main Results:

  • Successfully reconstructed the free parameters of the cubic mean-field Ising model.
  • Demonstrated the robustness of the inversion procedure in regions with unique solutions.
  • Confirmed the method's effectiveness even in the presence of multiple thermodynamic phases.

Conclusions:

  • The developed inversion technique is effective for parameter reconstruction in the cubic mean-field Ising model.
  • The method is reliable across different thermodynamic regimes, including those with phase transitions.