Monomers and Dimers

Ole J. Heilmann; Elliott H. Lieb

doi:10.1103/PhysRevLett.24.1412

Monomers and Dimers

Ole J. Heilmann, Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

125 Scopus citations

Abstract

We prove that the free energy of an arbitrary monomer-dimer system is analytic in the density and temperature for nonzero density, and hence that the system has no phase transition. This result can also be used to locate the z=e2βh roots of the Heisenberg ferromagnet or antiferromagnet at high temperature.

Original language	English (US)
Pages (from-to)	1412-1414
Number of pages	3
Journal	Physical review letters
Volume	24
Issue number	25
DOIs	https://doi.org/10.1103/PhysRevLett.24.1412
State	Published - 1970

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

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10.1103/PhysRevLett.24.1412

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title = "Monomers and Dimers",

abstract = "We prove that the free energy of an arbitrary monomer-dimer system is analytic in the density and temperature for nonzero density, and hence that the system has no phase transition. This result can also be used to locate the z=e2βh roots of the Heisenberg ferromagnet or antiferromagnet at high temperature.",

author = "Heilmann, {Ole J.} and Lieb, {Elliott H.}",

note = "Funding Information: Work partially supported by Statens Naturvidenskabelige Forskningsr{\aa}d Grant No. 511-208/69. Funding Information: Work partially supported by National Science Foundation Grant No. GP-9414. ",

year = "1970",

doi = "10.1103/PhysRevLett.24.1412",

language = "English (US)",

volume = "24",

pages = "1412--1414",

journal = "Physical Review Letters",

issn = "0031-9007",

publisher = "American Physical Society",

number = "25",

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T1 - Monomers and Dimers

AU - Heilmann, Ole J.

AU - Lieb, Elliott H.

N1 - Funding Information: Work partially supported by Statens Naturvidenskabelige Forskningsråd Grant No. 511-208/69. Funding Information: Work partially supported by National Science Foundation Grant No. GP-9414.

PY - 1970

Y1 - 1970

N2 - We prove that the free energy of an arbitrary monomer-dimer system is analytic in the density and temperature for nonzero density, and hence that the system has no phase transition. This result can also be used to locate the z=e2βh roots of the Heisenberg ferromagnet or antiferromagnet at high temperature.

AB - We prove that the free energy of an arbitrary monomer-dimer system is analytic in the density and temperature for nonzero density, and hence that the system has no phase transition. This result can also be used to locate the z=e2βh roots of the Heisenberg ferromagnet or antiferromagnet at high temperature.

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U2 - 10.1103/PhysRevLett.24.1412

DO - 10.1103/PhysRevLett.24.1412

M3 - Article

AN - SCOPUS:0014799509

SN - 0031-9007

VL - 24

SP - 1412

EP - 1414

JO - Physical Review Letters

JF - Physical Review Letters

IS - 25

ER -

Monomers and Dimers

Abstract

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