Phase transition in zero dimensions: A remark on the spherical model

Elliott H. Lieb; Colin J. Thompson

doi:10.1063/1.1664980

Phase transition in zero dimensions: A remark on the spherical model

Elliott H. Lieb, Colin J. Thompson

Mathematics

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Abstract

It is shown that the spherical model consisting of N spins with nonzero interaction between two spins only has a phase transition in the limit N → ∞. This is a counterexample to a suggestion of Kac which states that an Ising model will have a transition if the corresponding spherical model has a transition. Possible modifications of Kac's conjecture are suggested and discussed.

Original language	English (US)
Pages (from-to)	1403-1406
Number of pages	4
Journal	Journal of Mathematical Physics
Volume	10
Issue number	8
DOIs	https://doi.org/10.1063/1.1664980
State	Published - 1969

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.1664980

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title = "Phase transition in zero dimensions: A remark on the spherical model",

abstract = "It is shown that the spherical model consisting of N spins with nonzero interaction between two spins only has a phase transition in the limit N → ∞. This is a counterexample to a suggestion of Kac which states that an Ising model will have a transition if the corresponding spherical model has a transition. Possible modifications of Kac's conjecture are suggested and discussed.",

author = "Lieb, \{Elliott H.\} and Thompson, \{Colin J.\}",

year = "1969",

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journal = "Journal of Mathematical Physics",

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T2 - A remark on the spherical model

AU - Lieb, Elliott H.

AU - Thompson, Colin J.

PY - 1969

Y1 - 1969

N2 - It is shown that the spherical model consisting of N spins with nonzero interaction between two spins only has a phase transition in the limit N → ∞. This is a counterexample to a suggestion of Kac which states that an Ising model will have a transition if the corresponding spherical model has a transition. Possible modifications of Kac's conjecture are suggested and discussed.

AB - It is shown that the spherical model consisting of N spins with nonzero interaction between two spins only has a phase transition in the limit N → ∞. This is a counterexample to a suggestion of Kac which states that an Ising model will have a transition if the corresponding spherical model has a transition. Possible modifications of Kac's conjecture are suggested and discussed.

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U2 - 10.1063/1.1664980

DO - 10.1063/1.1664980

M3 - Article

AN - SCOPUS:36849101124

SN - 0022-2488

VL - 10

SP - 1403

EP - 1406

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 8

ER -

Phase transition in zero dimensions: A remark on the spherical model

Abstract

All Science Journal Classification (ASJC) codes

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