An analytic lower bound for the cubic-lattice dimer constant

Yair Lavi

An analytic lower bound for the cubic-lattice dimer constant

A mix of human-written and AI-generated textHuman understanding: all partsmath.CO — Combinatorics math-ph — Mathematical Physics

Contributed by Yair Lavi ↗

Version 1 / Nov 10, 2026 / CC BY 4.0

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.

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References

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P. Csikvári, ``Matchings in vertex-transitive bipartite graphs,'' Israel Journal of Mathematics 215 (2016), 99--134. doi:10.1007/s11856-016-1375-9 (https://doi.org/10.1007/s11856-016-1375-9). The cited numbering refers to the author's V5 version (https://csikvarip.web.elte.hu/matchings_vertex-transitive_V5), dated 31 March 2015.DOI
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Version history

v1 · 8 pagesSubmitted by Yair LaviInitial depositCurrentNov 08, 2026