A comparison of plane rotor and Ising models

M. Aizenman; B. Simon

doi:10.1016/0375-9601(80)90493-4

A comparison of plane rotor and Ising models

M. Aizenman, B. Simon

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

18 Scopus citations

Abstract

Let β_c^I be the critical inverse temperature in an Ising ferromagnet with pair interactions and let β_c^R be the critical temperatures in the plane rotor (classical xy model) with the same couplings. We prove that β_c^R ≥ 2β_c^I. This yields the lower bound β_c ≥ 0.88 for the Kosterlitz-Thouless transition.

Original language	English (US)
Pages (from-to)	281-282
Number of pages	2
Journal	Physics Letters A
Volume	76
Issue number	3-4
DOIs	https://doi.org/10.1016/0375-9601(80)90493-4
State	Published - Mar 31 1980

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

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10.1016/0375-9601(80)90493-4

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title = "A comparison of plane rotor and Ising models",

abstract = "Let βcI be the critical inverse temperature in an Ising ferromagnet with pair interactions and let βcR be the critical temperatures in the plane rotor (classical xy model) with the same couplings. We prove that βcR ≥ 2βcI. This yields the lower bound βc ≥ 0.88 for the Kosterlitz-Thouless transition.",

author = "M. Aizenman and B. Simon",

note = "Funding Information: 2 Also at Department of Mathematics; research partially sup-ported by US National Science Foundation under Grant MCS-78-01885. Funding Information: 1 Research partially supported by US National Science Founda-tion under Grant PHY-7825390.",

year = "1980",

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doi = "10.1016/0375-9601(80)90493-4",

language = "English (US)",

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AU - Aizenman, M.

AU - Simon, B.

N1 - Funding Information: 2 Also at Department of Mathematics; research partially sup-ported by US National Science Foundation under Grant MCS-78-01885. Funding Information: 1 Research partially supported by US National Science Founda-tion under Grant PHY-7825390.

PY - 1980/3/31

Y1 - 1980/3/31

N2 - Let βcI be the critical inverse temperature in an Ising ferromagnet with pair interactions and let βcR be the critical temperatures in the plane rotor (classical xy model) with the same couplings. We prove that βcR ≥ 2βcI. This yields the lower bound βc ≥ 0.88 for the Kosterlitz-Thouless transition.

AB - Let βcI be the critical inverse temperature in an Ising ferromagnet with pair interactions and let βcR be the critical temperatures in the plane rotor (classical xy model) with the same couplings. We prove that βcR ≥ 2βcI. This yields the lower bound βc ≥ 0.88 for the Kosterlitz-Thouless transition.

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U2 - 10.1016/0375-9601(80)90493-4

DO - 10.1016/0375-9601(80)90493-4

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SP - 281

EP - 282

JO - Physics Letters A

JF - Physics Letters A

IS - 3-4

ER -

A comparison of plane rotor and Ising models

Abstract

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