Dimers on two-dimensional lattices
Abstract
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 (44), honeycomb (63), triangular (36), kagome (3.6.3.6), 3-12 (3.122) and its dual [3.122], and 4-8 (4.82) and its dual Union Jack [4.82] Archimedean tilings. The occurrence and nature of phase transitions are also analyzed and discussed.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.