Phase transitions in quantum spin systems with isotropic and nonisotropic interactions

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

doi:10.1007/BF01106729

Phase transitions in quantum spin systems with isotropic and nonisotropic interactions

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

Mathematics

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

363 Scopus citations

Abstract

We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic spin 1/2 x-y model and the Heisenberg antiferromagnet with spin 1, 3/2,...and with nearest neighbor interactions on a simple cubic lattice are included.

Original language	English (US)
Pages (from-to)	335-383
Number of pages	49
Journal	Journal of Statistical Physics
Volume	18
Issue number	4
DOIs	https://doi.org/10.1007/BF01106729
State	Published - Apr 1978

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Heisenberg ferromagnet
Phase transitions

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10.1007/BF01106729

Cite this

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title = "Phase transitions in quantum spin systems with isotropic and nonisotropic interactions",

abstract = "We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic spin 1/2 x-y model and the Heisenberg antiferromagnet with spin 1, 3/2,...and with nearest neighbor interactions on a simple cubic lattice are included.",

keywords = "Heisenberg ferromagnet, Phase transitions",

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

year = "1978",

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T1 - Phase transitions in quantum spin systems with isotropic and nonisotropic interactions

AU - Dyson, Freeman J.

AU - Lieb, Elliott H.

AU - Simon, Barry

PY - 1978/4

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N2 - We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic spin 1/2 x-y model and the Heisenberg antiferromagnet with spin 1, 3/2,...and with nearest neighbor interactions on a simple cubic lattice are included.

AB - We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic spin 1/2 x-y model and the Heisenberg antiferromagnet with spin 1, 3/2,...and with nearest neighbor interactions on a simple cubic lattice are included.

KW - Heisenberg ferromagnet

KW - Phase transitions

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U2 - 10.1007/BF01106729

DO - 10.1007/BF01106729

M3 - Article

AN - SCOPUS:34250276209

SN - 0022-4715

VL - 18

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EP - 383

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 4

ER -

Phase transitions in quantum spin systems with isotropic and nonisotropic interactions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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