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Tensor renormalization group study of hard-disk models on a triangular lattice.

S S Akimenko1, V A Gorbunov1, A V Myshlyavtsev1

  • 1Department of Chemical Engineering, Omsk State Technical University, Prospekt Mira 11, Omsk 644050, Russian Federation.

Physical Review. E
|October 3, 2019
PubMed
Summary
This summary is machine-generated.

The tensor renormalization group (TRG) method accurately models hard disk systems on triangular lattices, outperforming the transfer-matrix method. This research explores phase transitions in molecular layers, offering insights into thermodynamics and lattice models.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • The tensor renormalization group (TRG) method is a powerful computational technique for studying statistical mechanics models.
  • Hard disk models on lattices approximate molecular layers and are relevant to understanding phase transitions.
  • Comparing TRG with transfer-matrix (TM) and exact methods is crucial for validating its accuracy and performance.

Purpose of the Study:

  • To evaluate the accuracy and performance of the TRG method for hard disk models on a triangular lattice.
  • To investigate the convergence of discrete hard disk models to the continuous model.
  • To calculate critical chemical potentials and characterize phase transitions for various exclusion models.

Main Methods:

  • Application of the tensor renormalization group (TRG) method to hard disk models with varying disk diameters.
  • Utilizing the transfer-matrix (TM) method for comparison and validation.
  • Benchmarking TRG against TM and exact results for nearest-neighbor exclusion (1NN) models.

Main Results:

  • TRG demonstrated high accuracy and superior performance compared to TM for the studied models.
  • Critical chemical potentials (μc) were computed for models with up to 5 nearest-neighbor exclusions (5NN).
  • First-order phase transitions were observed for 3NN and 5NN models, while 4NN showed a continuous phase transition.

Conclusions:

  • The TRG method is a reliable and efficient tool for analyzing hard disk systems and their phase transitions.
  • The study provides valuable data on critical chemical potentials and transition types for various exclusion models.
  • Findings contribute to understanding the thermodynamics of molecular layers and the behavior of lattice models.