Dimers on two-dimensional lattices

Details Dimers on two-dimensional lattices Dimers on two-dimensional lattices

2003-03-13

arxiv.org/abs/cond-mat/0303251v5

Int. Jour. Mod. Phys. B 20, 5357-5371 (2006).

Physics

Condensed Matter

Statistical Mechanics

Typos corrections in Eqs. (28), (32) and (43)

Scientific paper

We consider close-packed dimers, or perfect matchings, on two-dimensional regular lattices. We review known results and derive new expressions for the free energy, entropy, and the molecular freedom of dimers for a number of lattices including the simple-quartic (4^4), honeycomb (6^3), triangular (3^6), kagome (3.6.3.6), 3-12 (3.12^2) and its dual [3.12^2], and 4-8 (4.8^2) and its dual Union Jack [4.8^2] Archimedean tilings. The occurrence and nature of phase transitions are also analyzed and discussed.

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