Dimers on two-dimensional lattices

TL;DR

This paper reviews and derives new analytical expressions for the thermodynamic properties of close-packed dimers on various two-dimensional lattices, analyzing phase transitions and molecular freedom.

Contribution

It provides new formulas for free energy, entropy, and molecular freedom of dimers on multiple 2D lattices, expanding understanding of their statistical mechanics.

Findings

Derived new expressions for free energy and entropy.

Analyzed phase transition behaviors.

Compared properties across different lattice types.

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 (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.