DOI: 10.1063/1.1705162. Statistical Mechanics of Dimers on a Quadratic Lattice

Statistical Mechanics of Dimers on a Quadratic Lattice

10.1063/1.1705162

Crossref journal-article

AIP Publishing

Journal of Mathematical Physics (317)

Abstract

The partition function for the square lattice completely filled with dimers is analyzed for a finite n × m rectangular lattice with edges and for the corresponding lattice with periodic boundary conditions. The total free energy is calculated asymptotically for fixed ξ = n/m up to terms o(1/n2−δ) for any δ &gt; 0. The bulk terms proportional to nm, the surface terms proportional to (n + m) which vanish with periodic boundary conditions, and the constant terms which reveal a parity and shape dependence are expressed explicitly using dilogarithms and elliptic theta functions.

Bibliography

Ferdinand, A. E. (1967). Statistical Mechanics of Dimers on a Quadratic Lattice. Journal of Mathematical Physics, 8(12), 2332â2339.

Authors 1

Arthur E. Ferdinand (first)

References 10 Referenced 64

10.1103/PhysRev.152.190 / Phys. Rev. (1966)
10.1039/tf9373301272 / Trans. Faraday Soc. (1937)
{'key': '2023062717331703300_r3', 'first-page': '512', 'volume': 'A169', 'year': '1939', 'journal-title': 'Proc. Roy. Soc. (London)'} / Proc. Roy. Soc. (London) (1939)
10.1039/tf9444000306 / Trans. Faraday Soc. (1944)
10.1016/0031-8914(61)90063-5 / Physica (1961)
10.1103/PhysRev.124.1664 / Phys. Rev. (1961)
{'key': '2023062717331703300_r7', 'volume': '6', 'year': '1961', 'journal-title': 'Phil. Mag.'} / Phil. Mag. (1961)
10.1103/PhysRev.76.1232 / Phys. Rev. (1949)
{'key': '2023062717331703300_r9'}
{'key': '2023062717331703300_r10'}

Dates

Type	When
Created	20 years, 7 months ago (Jan. 6, 2005, 3:06 p.m.)
Deposited	2 years, 2 months ago (June 27, 2023, 3:11 p.m.)
Indexed	1 month, 3 weeks ago (July 7, 2025, 4:24 a.m.)
Issued	57 years, 8 months ago (Dec. 1, 1967)
Published	57 years, 8 months ago (Dec. 1, 1967)
Published Online	20 years, 8 months ago (Dec. 21, 2004)
Published Print	57 years, 8 months ago (Dec. 1, 1967)

Funders 0

None

BibTeX

@article{Ferdinand_1967, title={Statistical Mechanics of Dimers on a Quadratic Lattice}, volume={8}, ISSN={1089-7658}, url={http://dx.doi.org/10.1063/1.1705162}, DOI={10.1063/1.1705162}, number={12}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Ferdinand, Arthur E.}, year={1967}, month=dec, pages={2332–2339} }

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