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{
    "pk": 64910,
    "title": "The monopole-dimer model on Cartesian products of plane graphs",
    "subtitle": null,
    "abstract": "The monopole-dimer model is a signed variant of the monomer-dimer model which has determinantal structure. We extend the monopole-dimer model for planar graphs (Math. Phys. Anal. Geom., 2015) to Cartesian products thereof and show that the partition function of this model can be expressed as a determinant of a generalised signed adjacency matrix. We then show that the partition function is independent of the orientations of the planar graphs so long as the orientations are Pfaffian. When these planar graphs are bipartite, we show that the computation of the partition function becomes especially simple. We then give an explicit product formula for the partition function of three-dimensional grid graphs a la Kasteleyn and Temperley-Fischer, which turns out to be fourth power of a polynomial when all grid lengths are even. Finally, we generalise this product formula to \\(d\\) dimensions, again obtaining an explicit product formula. We conclude with a discussion on asymptotic formulas for the free energy and monopole densities.\n \nMathematics Subject Classifications: 82B20, 05A15, 05C70\n \nKeywords: Monopole-dimer model, cartesian products, determinantal formula, Kasteleyn orientation, bipartite, cycle decomposition, partition function, grid graphs, free energy",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Monopole-dimer model"
        },
        {
            "word": "cartesian products"
        },
        {
            "word": "determinantal formula"
        },
        {
            "word": "Kasteleyn orientation"
        },
        {
            "word": "bipartite"
        },
        {
            "word": "cycle decomposition"
        },
        {
            "word": "partition function"
        },
        {
            "word": "grid graphs"
        },
        {
            "word": "free energy"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/6gs2p4jx",
    "frozenauthors": [
        {
            "first_name": "Anita",
            "middle_name": "",
            "last_name": "Arora",
            "name_suffix": "",
            "institution": "Department of Mathematics, Indian Institute of Science, Bangalore 560012, India",
            "department": ""
        },
        {
            "first_name": "Arvind",
            "middle_name": "",
            "last_name": "Ayyer",
            "name_suffix": "",
            "institution": "Department of Mathematics, Indian Institute of Science, Bangalore 560012, India",
            "department": ""
        }
    ],
    "date_submitted": "2023-12-22T13:23:47Z",
    "date_accepted": "2023-12-22T13:23:47Z",
    "date_published": "2023-12-22T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64910/galley/49720/download/"
        }
    ]
}