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Multiple phase transitions in extended hard-core lattice gas models in two dimensions
1The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India.
Summary
The k-nearest neighbor (k-NN) hard-core lattice gas model exhibits multiple phase transitions at higher densities for specific k values. This finding resolves a long-standing puzzle regarding the 4-NN model
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Computational Physics
Background:
- The k-nearest neighbor (k-NN) hard-core lattice gas model simulates hard-disk systems on a lattice.
- Previous studies indicated only a single phase transition in this lattice model, unlike the two-step freezing in hard-disk systems.
Purpose of the Study:
- To investigate the phase transition behavior of the k-NN hard-core lattice gas model at higher densities.
- To resolve the discrepancy between theoretical expectations and observed transitions, particularly for the 4-NN model.
Main Methods:
- Monte Carlo simulations were employed to study the model's behavior.
- High-density expansions of free energy and density were utilized for theoretical analysis.
Main Results:
- Multiple phase transitions were identified for specific k values (e.g., k = 4, 10, 11, 14, ...) with increasing density.
- Monte Carlo simulations confirmed these multiple transitions for k = 4 through 11.
- The study explains the continuous transition observed in the 4-NN model, which was previously unexpected.
Conclusions:
- The k-NN hard-core lattice gas model exhibits complex phase behavior with multiple transitions at higher densities for certain k.
- This research clarifies the phase transition mechanisms in lattice gas models and their relation to continuous systems.
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