Phase transitions in the quantum Heisenberg model

Freeman J. Dyson; Elliott H. Lieb; Barry Simon

doi:10.1103/PhysRevLett.37.120

Phase transitions in the quantum Heisenberg model

Freeman J. Dyson
, Elliott H. Lieb
, Barry Simon

Mathematics

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

44 Scopus citations

Abstract

We rigorously prove that in three or more dimensions, the nearest-neighbor, simple-cubic, ferromagnetic, quantum Heisenberg model of spin S (=12, 1, ...) has a phase transition at nonzero temperature.

Original language	English (US)
Pages (from-to)	120-123
Number of pages	4
Journal	Physical review letters
Volume	37
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevLett.37.120
State	Published - 1976

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1103/PhysRevLett.37.120

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@article{983b3001d2f4436fa84c3eccc004b310,

title = "Phase transitions in the quantum Heisenberg model",

abstract = "We rigorously prove that in three or more dimensions, the nearest-neighbor, simple-cubic, ferromagnetic, quantum Heisenberg model of spin S (=12, 1, ...) has a phase transition at nonzero temperature.",

author = "Dyson, \{Freeman J.\} and Lieb, \{Elliott H.\} and Barry Simon",

note = "Funding Information: Alfred Sloan Fellow. Research supported by U. S. National Science Foundation Grant No. GP-39048. Funding Information: Research supported by U. S. National Science Foundation Grant No. GP-40768X. Funding Information: Research supported by U. S. National Science Foundation Grant No. MCS 75-21648. ",

year = "1976",

doi = "10.1103/PhysRevLett.37.120",

language = "English (US)",

volume = "37",

pages = "120--123",

journal = "Physical review letters",

issn = "0031-9007",

publisher = "American Physical Society",

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TY - JOUR

T1 - Phase transitions in the quantum Heisenberg model

AU - Dyson, Freeman J.

AU - Lieb, Elliott H.

AU - Simon, Barry

N1 - Funding Information: Alfred Sloan Fellow. Research supported by U. S. National Science Foundation Grant No. GP-39048. Funding Information: Research supported by U. S. National Science Foundation Grant No. GP-40768X. Funding Information: Research supported by U. S. National Science Foundation Grant No. MCS 75-21648.

PY - 1976

Y1 - 1976

N2 - We rigorously prove that in three or more dimensions, the nearest-neighbor, simple-cubic, ferromagnetic, quantum Heisenberg model of spin S (=12, 1, ...) has a phase transition at nonzero temperature.

AB - We rigorously prove that in three or more dimensions, the nearest-neighbor, simple-cubic, ferromagnetic, quantum Heisenberg model of spin S (=12, 1, ...) has a phase transition at nonzero temperature.

UR - https://www.scopus.com/pages/publications/25344448933

UR - https://www.scopus.com/pages/publications/25344448933#tab=citedBy

U2 - 10.1103/PhysRevLett.37.120

DO - 10.1103/PhysRevLett.37.120

M3 - Article

AN - SCOPUS:25344448933

SN - 0031-9007

VL - 37

SP - 120

EP - 123

JO - Physical review letters

JF - Physical review letters

IS - 3

ER -

Phase transitions in the quantum Heisenberg model

Abstract

All Science Journal Classification (ASJC) codes

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