DOI: 10.1063/1.524404. The use of anticommuting variable integrals in statistical mechanics. I. The computation of partition functions

The use of anticommuting variable integrals in statistical mechanics. I. The computation of partition functions

10.1063/1.524404

Crossref journal-article

AIP Publishing

Journal of Mathematical Physics (317)

Abstract

Integrals over anticommuting variables are use to rewrite partition functions as fermionic field theories. The method is used to solve the two-dimensional Ising model, the planar close-packed dimer problems, and the free-fermion eight vertex model.

Bibliography

Samuel, S. (1980). The use of anticommuting variable integrals in statistical mechanics. I. The computation of partition functions. Journal of Mathematical Physics, 21(12), 2806â2814.

Authors 1

Stuart Samuel (first)

References 20 Referenced 132

{'key': '2024021013390090700_r1', 'first-page': '1916', 'volume': '18', 'year': '1978', 'journal-title': 'Phys. Rev. D'} / Phys. Rev. D (1978)
10.1007/BF02745446 / Nuovo Cimento (1956)
10.1063/1.523809 / J. Math. Phys. (1978)
{'key': '2024021013390090700_r4'}
{'key': '2024021013390090700_r5'}
{'key': '2024021013390090700_r6'}
{'key': '2024021013390090700_r7'}
10.1103/RevModPhys.36.856 / Rev. Mod. Phys. (1964)
{'key': '2024021013390090700_r9'}
10.1063/1.1704933 / J. Math. Phys. (1966)
{'key': '2024021013390090700_r11'}
{'key': '2024021013390090700_r11a'}
{'key': '2024021013390090700_r12'}
{'key': '2024021013390090700_r14'}
{'key': '2024021013390090700_r15'}
{'key': '2024021013390090700_r16'}
{'key': '2024021013390090700_r17'}
10.1103/PhysRevB.2.723 / Phys. Rev. B (1970)
{'key': '2024021013390090700_r19', 'first-page': '117', 'volume': '65', 'year': '1964', 'journal-title': 'Phys. Rev.'} / Phys. Rev. (1964)
10.1063/1.1703953 / J. Math. Phys. (1963)

Dates

Type	When
Created	22 years, 5 months ago (March 7, 2003, 12:33 p.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 10:09 a.m.)
Indexed	3 weeks ago (Aug. 6, 2025, 8:33 a.m.)
Issued	44 years, 8 months ago (Dec. 1, 1980)
Published	44 years, 8 months ago (Dec. 1, 1980)
Published Print	44 years, 8 months ago (Dec. 1, 1980)

Funders 0

None

BibTeX

@article{Samuel_1980, title={The use of anticommuting variable integrals in statistical mechanics. I. The computation of partition functions}, volume={21}, ISSN={1089-7658}, url={http://dx.doi.org/10.1063/1.524404}, DOI={10.1063/1.524404}, number={12}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Samuel, Stuart}, year={1980}, month=dec, pages={2806–2814} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        6
      ]
    ],
    "date-time": "2025-08-06T12:33:23Z",
    "timestamp": 1754483603881
  },
  "reference-count": 20,
  "publisher": "AIP Publishing",
  "issue": "12",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1980,
        12,
        1
      ]
    ]
  },
  "abstract": "<jats:p>Integrals over anticommuting variables are use to rewrite partition functions as fermionic field theories. The method is used to solve the two-dimensional Ising model, the planar close-packed dimer problems, and the free-fermion eight vertex model.</jats:p>",
  "DOI": "10.1063/1.524404",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2003,
        3,
        7
      ]
    ],
    "date-time": "2003-03-07T17:33:22Z",
    "timestamp": 1047058402000
  },
  "page": "2806-2814",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 132,
  "title": "The use of anticommuting variable integrals in statistical mechanics. I. The computation of partition functions",
  "prefix": "10.1063",
  "volume": "21",
  "author": [
    {
      "given": "Stuart",
      "family": "Samuel",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Lawrence Berkeley Laboratory, Unviersity of California, Berkeley, California 94720"
        },
        {
          "name": "Institute for Advanced Study, Princeton, New Jersey 08540"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024021013390090700_r1",
      "first-page": "1916",
      "volume": "18",
      "year": "1978",
      "journal-title": "Phys. Rev. D"
    },
    {
      "key": "2024021013390090700_r2",
      "doi-asserted-by": "crossref",
      "first-page": "231",
      "DOI": "10.1007/BF02745446",
      "volume": "4",
      "year": "1956",
      "journal-title": "Nuovo Cimento"
    },
    {
      "key": "2024021013390090700_r3",
      "doi-asserted-by": "crossref",
      "first-page": "1438",
      "DOI": "10.1063/1.523809",
      "volume": "19",
      "year": "1978",
      "journal-title": "J. Math. Phys."
    },
    {
      "key": "2024021013390090700_r4"
    },
    {
      "key": "2024021013390090700_r5"
    },
    {
      "key": "2024021013390090700_r6"
    },
    {
      "key": "2024021013390090700_r7"
    },
    {
      "key": "2024021013390090700_r8",
      "doi-asserted-by": "crossref",
      "first-page": "856",
      "DOI": "10.1103/RevModPhys.36.856",
      "volume": "36",
      "year": "1964",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2024021013390090700_r9"
    },
    {
      "key": "2024021013390090700_r10",
      "doi-asserted-by": "crossref",
      "first-page": "305",
      "DOI": "10.1063/1.1704933",
      "volume": "7",
      "year": "1966",
      "journal-title": "J. Math. Phys."
    },
    {
      "key": "2024021013390090700_r11"
    },
    {
      "key": "2024021013390090700_r11a"
    },
    {
      "key": "2024021013390090700_r12"
    },
    {
      "key": "2024021013390090700_r14"
    },
    {
      "key": "2024021013390090700_r15"
    },
    {
      "key": "2024021013390090700_r16"
    },
    {
      "key": "2024021013390090700_r17"
    },
    {
      "key": "2024021013390090700_r18",
      "doi-asserted-by": "crossref",
      "first-page": "723",
      "DOI": "10.1103/PhysRevB.2.723",
      "volume": "2",
      "year": "1970",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024021013390090700_r19",
      "first-page": "117",
      "volume": "65",
      "year": "1964",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024021013390090700_r20",
      "doi-asserted-by": "crossref",
      "first-page": "287",
      "DOI": "10.1063/1.1703953",
      "volume": "4",
      "year": "1963",
      "journal-title": "J. Math. Phys."
    }
  ],
  "container-title": "Journal of Mathematical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jmp/article-pdf/21/12/2806/19003406/2806_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jmp/article-pdf/21/12/2806/19003406/2806_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        10
      ]
    ],
    "date-time": "2024-02-10T15:09:13Z",
    "timestamp": 1707577753000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jmp/article/21/12/2806/444617/The-use-of-anticommuting-variable-integrals-in"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1980,
        12,
        1
      ]
    ]
  },
  "references-count": 20,
  "journal-issue": {
    "issue": "12",
    "published-print": {
      "date-parts": [
        [
          1980,
          12,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.524404",
  "relation": {},
  "ISSN": [
    "0022-2488",
    "1089-7658"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1980,
        12
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1980,
        12,
        1
      ]
    ]
  }
}