bibkey: heilmannlieb1972monomerdimer authors: Ole J. Heilmann and Elliott H. Lieb year: 1972 title: Theory of monomer-dimer systems doi: 10.1007/BF01877590 claim: With nonnegative dimer activities, the monomer-activity partition polynomial has only imaginary zeros; the weighted-path matching specialization has strictly negative zeros in the dimer generating variable. strata_touched:

• D5/S3/Quantum/FockSpace/ForbiddenNeighbourDeterminant license: citation-only triage: anchor

Theory of monomer-dimer systems

The Princeton publication record reproduces the abstract of Heilmann and Lieb, Communications in Mathematical Physics 25 (1972), 190-232. Its stated main result places the zeros of the monomer-activity polynomial on the imaginary axis when the dimer activities are nonnegative. It explicitly includes zero activities. No theorem number is asserted here.

The repository specializes matching configurations to a finite path. Its generating variable counts dimers, so the corresponding zeros are negative real numbers. The repository supplies the explicit odd/even square-root bidiagonal Gram realization and the separate normalized configuration-space quantum readout. This note attributes the matching-polynomial zero principle; it does not attribute that full matrix-and-readout packaging to the paper.

Verified locator

• DOI: https://doi.org/10.1007/BF01877590
• Princeton record and abstract: https://collaborate.princeton.edu/en/publications/theory-of-monomer-dimer-systems-2/
• Crossref record: https://api.crossref.org/works/10.1007/BF01877590

On 2026-09-06, both HTTP requests returned exit 0. The Crossref record verified the title, authors, year, journal, pages and DOI. The Princeton abstract states the imaginary-axis result and the nonnegative-activity hypothesis verbatim.