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Tensor network construction for lattice gas models: Hard-core and triangular lattice models.

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This study explores two tensor network construction methods for lattice models. Different construction approaches impact calculation accuracy, refining phase transition estimates for 4 nearest-neighbor (NN) and 5NN models.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics

Background:

  • Tensor network representation is key for analyzing complex lattice model thermodynamics.
  • Multiple tensor network constructions exist for the same model, potentially affecting results.

Purpose of the Study:

  • Investigate how different tensor network construction methods influence calculation accuracy.
  • Analyze adsorption isotherms, entropy, and heat capacity for 4NN, 5NN, and a modified 4NN model.
  • Improve phase transition point estimations and identify phase transitions in complex models.

Main Methods:

  • Developed and compared two distinct tensor network construction techniques.
  • Studied 4 nearest-neighbor (NN) and 5NN lattice models with hard-core repulsions.
  • Analyzed a 4NN model with finite repulsions involving a fifth neighbor.

Main Results:

  • Demonstrated that the tensor network construction process significantly affects thermodynamic calculation accuracy.
  • Obtained adsorption isotherms, entropy, and heat capacity graphs for all studied models.
  • Refined phase transition point estimates for 4NN and 5NN models and identified two first-order phase transitions in the finite interaction model.

Conclusions:

  • The choice of tensor network construction method is critical for accurate thermodynamic analysis of lattice models.
  • The study provides improved phase transition data and reveals complex phase behavior in models with finite interactions.