Entropy of rigid k-mers on a square lattice

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics

Background:

• Entropy calculations are crucial for understanding phase transitions and material properties.
• Estimating entropy for lattice-confined systems, like k-mers, presents significant computational challenges.

Purpose of the Study:

• To estimate the entropy of k-mers completely covering a square lattice.
• To introduce and validate a novel 'profile method' for transfer matrix construction.
• To compare results with existing literature and theoretical predictions.

Main Methods:

• Utilized the transfer matrix technique with periodical and helical boundary conditions.
• Developed a 'profile method' for transfer matrix construction, reducing matrix dimensions.
• Calculated entropy for k-mer sizes from k=2 to k=10.

Main Results:

• The 'profile method' proved effective, yielding smaller matrices than traditional approaches.
• Results for dimers (k=2) and trimers (k=3) are consistent with exact and literature values.
• Calculated entropies align with the asymptotic behavior predicted for large k-mers (k≫1).

Conclusions:

• The 'profile method' is a valuable advancement for entropy calculations in lattice systems.
• The study provides reliable entropy estimates for k-mers on a square lattice across various sizes.
• Findings support existing theoretical models for large k-mer systems.