Translation invariance and instability of phase coexistence in the two dimensional Ising system

Michael Aizenman

doi:10.1007/BF01942696

Translation invariance and instability of phase coexistence in the two dimensional Ising system

Michael Aizenman

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

108 Scopus citations

Abstract

It is shown that any Gibbs state of the two dimensional ferromagnetic Ising system is of the form λμ₊+(1-λ)μ_-, with some λ∈ [0, 1]. This excludes the possibility of a locally stable phase coexistence and of translation symmetry breaking, which are known to occur in higher dimensions. Use is made in the proof of the stochastic aspects of the geometry of the interface lines.

Original language	English (US)
Pages (from-to)	83-94
Number of pages	12
Journal	Communications In Mathematical Physics
Volume	73
Issue number	1
DOIs	https://doi.org/10.1007/BF01942696
State	Published - May 1980

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01942696

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title = "Translation invariance and instability of phase coexistence in the two dimensional Ising system",

abstract = "It is shown that any Gibbs state of the two dimensional ferromagnetic Ising system is of the form λμ++(1-λ)μ-, with some λ∈ [0, 1]. This excludes the possibility of a locally stable phase coexistence and of translation symmetry breaking, which are known to occur in higher dimensions. Use is made in the proof of the stochastic aspects of the geometry of the interface lines.",

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AB - It is shown that any Gibbs state of the two dimensional ferromagnetic Ising system is of the form λμ++(1-λ)μ-, with some λ∈ [0, 1]. This excludes the possibility of a locally stable phase coexistence and of translation symmetry breaking, which are known to occur in higher dimensions. Use is made in the proof of the stochastic aspects of the geometry of the interface lines.

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Translation invariance and instability of phase coexistence in the two dimensional Ising system

Abstract

All Science Journal Classification (ASJC) codes

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