DOI: 10.1063/1.330231. First- and second-order phase transitions in Potts models: Competing mechanisms (invited)

First- and second-order phase transitions in Potts models: Competing mechanisms (invited)

10.1063/1.330231

Crossref journal-article

AIP Publishing

Journal of Applied Physics (317)

Abstract

Many condensed matter systems, ranging from adsorbed surfaces to bulk magnets, are microscopically modelled by interacting q-state Potts spins, arrayed in d dimensions. A changeover from second-order phase transitions at q≤qc(d) to first-order transitions at q≳qc can be understood as a condensation of effect vacancies, which are patches of local disorder favored by entropy. Accordingly, the renormalization-group treatment of Potts models is within context of Potts-lattice-gas models, where critical and tricritical fixed points occur at low q, but merge and annihilate at qc. This picture has led to exact tricritical exponents in two dimensions. It is also consistent with recent experimental results on intercalated systems in three dimensions. Effective vacancies in pure Potts models have also been studied by Monte Carlo simulation. Their effective chemical potential can be controlled by a four-point interaction, which proved useful in Monte Carlo renormalization-group studies.

Bibliography

Berker, A. N., & Andelman, D. (1982). First- and second-order phase transitions in Potts models: Competing mechanisms (invited). Journal of Applied Physics, 53(11), 7923â7926.

Authors 2

A. Nihat Berker (first)
David Andelman (additional)

References 31 Referenced 18

10.1017/S0305004100027419 / Proc. Camb. Philos. Soc. (1952)
10.1103/RevModPhys.54.235 / Rev. Mod. Phys. (1982)
{'key': '2024020501273757400_r2'}
10.1088/0022-3719/11/5/007 / J. Phys. C (1978)
10.1016/0375-9601(75)90766-5 / Phys. Lett. A (1975)
10.1103/PhysRevLett.38.33 / Phys. Rev. Lett. (1977)
10.1103/PhysRevB.20.2818 / Phys. Rev. B (1979)
10.1063/1.437429 / J. Chem. Phys. (1979)
{'key': '2024020501273757400_r8', 'first-page': '11', 'volume': '26', 'year': '1969', 'journal-title': 'J. Phys. Soc. Japan Suppl.'} / J. Phys. Soc. Japan Suppl. (1969)
{'key': '2024020501273757400_r9', 'first-page': '26', 'volume': '11', 'year': '1937', 'journal-title': 'Phys. Z. Sowjetunion'} / Phys. Z. Sowjetunion (1937)
{'key': '2024020501273757400_r9a'}
{'key': '2024020501273757400_r9b'}
10.1088/0022-3719/6/23/005 / J. Phys. C (1973)
10.1088/0305-4470/6/9/007 / J. Phys. A (1973)
{'key': '2024020501273757400_r12'}
10.1103/PhysRevLett.43.737 / Phys. Rev. Lett. (1979)
10.1103/PhysRevB.17.3650 / Phys. Rev. B (1978)
10.1088/0305-4470/13/2/006 / J. Phys. A (1980)
10.1007/BF01301522 / Z. Phys. B (1980)
10.1088/0305-4470/13/11/007 / J. Phys. A (1980)
10.1088/0305-4470/14/4/005 / J. Phys. A (1981)
10.1103/PhysRevB.23.6055 / Phys. Rev. B (1981)
{'key': '2024020501273757400_r18', 'first-page': '1887', 'volume': '12', 'year': '1979', 'journal-title': 'J. Phys. A'} / J. Phys. A (1979)
10.1088/0305-4470/13/6/005 / J. Phys. A (1980)
10.1103/PhysRevB.22.2579 / Phys. Rev. B (1980)
{'key': '2024020501273757400_r20', 'first-page': '429', 'volume': '23', 'year': '1980', 'journal-title': 'Phys. Rev. B'} / Phys. Rev. B (1980)
10.1088/0305-4470/15/1/028 / J. Phys. A (1982)
10.1103/PhysRevB.24.6732 / Phys. Rev. B (1981)
{'key': '2024020501273757400_r22'}
{'key': '2024020501273757400_r23'}
10.1103/PhysRevLett.48.156 / Phys. Rev. Lett. (1982)

Dates

Type	When
Created	22 years, 6 months ago (Feb. 14, 2003, 6:21 p.m.)
Deposited	1 year, 6 months ago (Feb. 4, 2024, 8:27 p.m.)
Indexed	1 year, 6 months ago (Feb. 4, 2024, 8:40 p.m.)
Issued	42 years, 9 months ago (Nov. 1, 1982)
Published	42 years, 9 months ago (Nov. 1, 1982)
Published Print	42 years, 9 months ago (Nov. 1, 1982)

Funders 0

None

BibTeX

@article{Berker_1982, title={First- and second-order phase transitions in Potts models: Competing mechanisms (invited)}, volume={53}, ISSN={1089-7550}, url={http://dx.doi.org/10.1063/1.330231}, DOI={10.1063/1.330231}, number={11}, journal={Journal of Applied Physics}, publisher={AIP Publishing}, author={Berker, A. Nihat and Andelman, David}, year={1982}, month=nov, pages={7923–7926} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2024,
        2,
        5
      ]
    ],
    "date-time": "2024-02-05T01:40:53Z",
    "timestamp": 1707097253677
  },
  "reference-count": 31,
  "publisher": "AIP Publishing",
  "issue": "11",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1982,
        11,
        1
      ]
    ]
  },
  "abstract": "<jats:p>Many condensed matter systems, ranging from adsorbed surfaces to bulk magnets, are microscopically modelled by interacting q-state Potts spins, arrayed in d dimensions. A changeover from second-order phase transitions at q\u2264qc(d) to first-order transitions at q\u2273qc can be understood as a condensation of effect vacancies, which are patches of local disorder favored by entropy. Accordingly, the renormalization-group treatment of Potts models is within context of Potts-lattice-gas models, where critical and tricritical fixed points occur at low q, but merge and annihilate at qc. This picture has led to exact tricritical exponents in two dimensions. It is also consistent with recent experimental results on intercalated systems in three dimensions. Effective vacancies in pure Potts models have also been studied by Monte Carlo simulation. Their effective chemical potential can be controlled by a four-point interaction, which proved useful in Monte Carlo renormalization-group studies.</jats:p>",
  "DOI": "10.1063/1.330231",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2003,
        2,
        14
      ]
    ],
    "date-time": "2003-02-14T23:21:59Z",
    "timestamp": 1045264919000
  },
  "page": "7923-7926",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 18,
  "title": "First- and second-order phase transitions in Potts models: Competing mechanisms (invited)",
  "prefix": "10.1063",
  "volume": "53",
  "author": [
    {
      "given": "A. Nihat",
      "family": "Berker",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139"
        }
      ]
    },
    {
      "given": "David",
      "family": "Andelman",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020501273757400_r1",
      "doi-asserted-by": "crossref",
      "first-page": "106",
      "DOI": "10.1017/S0305004100027419",
      "volume": "48",
      "year": "1952",
      "journal-title": "Proc. Camb. Philos. Soc."
    },
    {
      "key": "2024020501273757400_r1a",
      "doi-asserted-by": "crossref",
      "first-page": "235",
      "DOI": "10.1103/RevModPhys.54.235",
      "volume": "54",
      "year": "1982",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2024020501273757400_r2"
    },
    {
      "key": "2024020501273757400_r3",
      "doi-asserted-by": "crossref",
      "first-page": "L183",
      "DOI": "10.1088/0022-3719/11/5/007",
      "volume": "11",
      "year": "1978",
      "journal-title": "J. Phys. C"
    },
    {
      "key": "2024020501273757400_r4",
      "doi-asserted-by": "crossref",
      "first-page": "353",
      "DOI": "10.1016/0375-9601(75)90766-5",
      "volume": "54",
      "year": "1975",
      "journal-title": "Phys. Lett. A"
    },
    {
      "key": "2024020501273757400_r5",
      "doi-asserted-by": "crossref",
      "first-page": "33",
      "DOI": "10.1103/PhysRevLett.38.33",
      "volume": "38",
      "year": "1977",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024020501273757400_r6",
      "doi-asserted-by": "crossref",
      "first-page": "2818",
      "DOI": "10.1103/PhysRevB.20.2818",
      "volume": "20",
      "year": "1979",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024020501273757400_r7",
      "doi-asserted-by": "crossref",
      "first-page": "5555",
      "DOI": "10.1063/1.437429",
      "volume": "70",
      "year": "1979",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020501273757400_r8",
      "first-page": "11",
      "volume": "26",
      "year": "1969",
      "journal-title": "J. Phys. Soc. Japan Suppl."
    },
    {
      "key": "2024020501273757400_r9",
      "first-page": "26",
      "volume": "11",
      "year": "1937",
      "journal-title": "Phys. Z. Sowjetunion"
    },
    {
      "key": "2024020501273757400_r9a"
    },
    {
      "key": "2024020501273757400_r9b"
    },
    {
      "key": "2024020501273757400_r10",
      "doi-asserted-by": "crossref",
      "first-page": "L445",
      "DOI": "10.1088/0022-3719/6/23/005",
      "volume": "6",
      "year": "1973",
      "journal-title": "J. Phys. C"
    },
    {
      "key": "2024020501273757400_r11",
      "doi-asserted-by": "crossref",
      "first-page": "1310",
      "DOI": "10.1088/0305-4470/6/9/007",
      "volume": "6",
      "year": "1973",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024020501273757400_r12"
    },
    {
      "key": "2024020501273757400_r13",
      "doi-asserted-by": "crossref",
      "first-page": "737",
      "DOI": "10.1103/PhysRevLett.43.737",
      "volume": "43",
      "year": "1979",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024020501273757400_r14",
      "doi-asserted-by": "crossref",
      "first-page": "3650",
      "DOI": "10.1103/PhysRevB.17.3650",
      "volume": "17",
      "year": "1978",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024020501273757400_r15",
      "doi-asserted-by": "crossref",
      "first-page": "L31",
      "DOI": "10.1088/0305-4470/13/2/006",
      "volume": "13",
      "year": "1980",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024020501273757400_r15a",
      "doi-asserted-by": "crossref",
      "first-page": "159",
      "DOI": "10.1007/BF01301522",
      "volume": "39",
      "year": "1980",
      "journal-title": "Z. Phys. B"
    },
    {
      "key": "2024020501273757400_r16",
      "doi-asserted-by": "crossref",
      "first-page": "L413",
      "DOI": "10.1088/0305-4470/13/11/007",
      "volume": "13",
      "year": "1980",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024020501273757400_r16a",
      "doi-asserted-by": "crossref",
      "first-page": "L91",
      "DOI": "10.1088/0305-4470/14/4/005",
      "volume": "14",
      "year": "1981",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024020501273757400_r17",
      "doi-asserted-by": "crossref",
      "first-page": "6055",
      "DOI": "10.1103/PhysRevB.23.6055",
      "volume": "23",
      "year": "1981",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024020501273757400_r18",
      "first-page": "1887",
      "volume": "12",
      "year": "1979",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024020501273757400_r19",
      "doi-asserted-by": "crossref",
      "first-page": "L189",
      "DOI": "10.1088/0305-4470/13/6/005",
      "volume": "13",
      "year": "1980",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024020501273757400_r19a",
      "doi-asserted-by": "crossref",
      "first-page": "2579",
      "DOI": "10.1103/PhysRevB.22.2579",
      "volume": "22",
      "year": "1980",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024020501273757400_r20",
      "first-page": "429",
      "volume": "23",
      "year": "1980",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024020501273757400_r20a",
      "doi-asserted-by": "crossref",
      "first-page": "199",
      "DOI": "10.1088/0305-4470/15/1/028",
      "volume": "15",
      "year": "1982",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024020501273757400_r21",
      "doi-asserted-by": "crossref",
      "first-page": "6732",
      "DOI": "10.1103/PhysRevB.24.6732",
      "volume": "24",
      "year": "1981",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024020501273757400_r22"
    },
    {
      "key": "2024020501273757400_r23"
    },
    {
      "key": "2024020501273757400_r24",
      "doi-asserted-by": "crossref",
      "first-page": "156",
      "DOI": "10.1103/PhysRevLett.48.156",
      "volume": "48",
      "year": "1982",
      "journal-title": "Phys. Rev. Lett."
    }
  ],
  "container-title": "Journal of Applied Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jap/article-pdf/53/11/7923/18399439/7923_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jap/article-pdf/53/11/7923/18399439/7923_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        5
      ]
    ],
    "date-time": "2024-02-05T01:27:49Z",
    "timestamp": 1707096469000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jap/article/53/11/7923/11088/First-and-second-order-phase-transitions-in-Potts"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1982,
        11,
        1
      ]
    ]
  },
  "references-count": 31,
  "journal-issue": {
    "issue": "11",
    "published-print": {
      "date-parts": [
        [
          1982,
          11,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.330231",
  "relation": {},
  "ISSN": [
    "0021-8979",
    "1089-7550"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1982,
        11,
        1
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1982,
        11,
        1
      ]
    ]
  }
}