An analytic lower bound for the cubic-lattice dimer constant

We prove that the close-packed dimer entropy per site ℓ3 of the simple cubic lattice satisfies ℓ3 ≥ ½ log(3125/1296) + 47/10000 = 0.444775842629…. This exceeds the previous best published lower bound, obtained by Csikvári of 0.441075842629…. The proof uses finite matching inequalities and elementary integration, without numerical quadrature or a computational certificate.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-06
DOI
https://doi.org/10.5281/zenodo.23192271
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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preprint

An analytic lower bound for the cubic-lattice dimer constant

Yair Lavi
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

An analytic lower bound for the cubic-lattice dimer constant

Yair Lavi
preprint en

Abstract

We prove that the close-packed dimer entropy per site ℓ3 of the simple cubic lattice satisfies ℓ3 ≥ ½ log(3125/1296) + 47/10000 = 0.444775842629…. This exceeds the previous best published lower bound, obtained by Csikvári of 0.441075842629…. The proof uses finite matching inequalities and elementary integration, without numerical quadrature or a computational certificate.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
DOIOpen Access PDFOpenAlex
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An analytic lower bound for the cubic-lattice dimer constant — Yair Lavi · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS