An analytic lower bound for the cubic-lattice dimer constant
2026-10-06
Research publication
An analytic lower bound for the cubic-lattice dimer constant
Preprint
- Original date
- Authors
- Yair Lavi
- Statistical mechanics
- Combinatorics
- Dimer model
- Matching entropy
Abstract
We prove that the close-packed dimer entropy per site \(\ell_3\) of the simple cubic lattice satisfies
\[ \ell_3\ge\frac12\log\frac{3125}{1296}+\frac{47}{10000}=0.444775842629\ldots. \]
This exceeds the previous best published lower bound, obtained by Csikvári of \({0.441075842629\ldots}\). The proof uses finite matching inequalities and elementary integration, without numerical quadrature or a computational certificate.