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Researchers explored percolation on dimer-covered lattices, a novel area. They found that random dimer coverings on square and triangular lattices exhibit distinct percolation thresholds, with square lattices showing greater "frustration".

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Area of Science:

  • Statistical Physics
  • Discrete Mathematics
  • Materials Science

Background:

  • Dimer coverings are well-studied in various scientific fields.
  • Percolation on dimer-covered lattices remains underexplored, especially for fully covered lattices.

Purpose of the Study:

  • To introduce a method for generating random dimer coverings.
  • To compute bond percolation thresholds on random and ordered dimer coverings of square and triangular lattices.

Main Methods:

  • Developed a procedure for generating random dimer coverings.
  • Calculated bond percolation thresholds on square and triangular lattices with random and ordered dimer coverings.

Main Results:

  • Obtained percolation thresholds for random coverings: p_c=0.367713(2) for square and p_c=0.235340(1) for triangular lattices.
  • Observed greater percolation frustration in the lower-coordination square lattice.
  • Found no correlation between long-range order and percolation threshold in square lattices; a shifted covering showed an unusually low threshold.

Conclusions:

  • Percolation thresholds are sensitive to lattice coordination and dimer covering details.
  • Highly coordinated lattices like the triangular lattice show less sensitivity to microscopic covering variations.
  • Ordered dimer coverings can significantly alter percolation behavior, sometimes counterintuitively.