On the renormalized coupling constant and the susceptibility in φ44 field theory and the Ising model in four dimensions

Michael Aizenman; Ross Graham

doi:10.1016/0550-3213(83)90053-6

On the renormalized coupling constant and the susceptibility in φ₄⁴ field theory and the Ising model in four dimensions

Michael Aizenman, Ross Graham

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

55 Scopus citations

Abstract

We discuss the euclidean φ₄⁴ field theory, and the critical behavior in ferromagnetic systems in four dimensions. It is rigorously shown that there are at most logarithmic corrections to the mean field law in the behavior of the magnetic susceptibility _X = ΣS₂(0, x). Furthermore, if any such corrections are present in a continuum limit which is used to construct a φ₄⁴ field theory, the limiting theory would be non-interacting. Our analysis extends to ferromagnetic systems of variables which belong to the Griffiths-Simon class.

Original language	English (US)
Pages (from-to)	261-288
Number of pages	28
Journal	Nuclear Physics, Section B
Volume	225
Issue number	2
DOIs	https://doi.org/10.1016/0550-3213(83)90053-6
State	Published - Oct 31 1983
Externally published	Yes

All Science Journal Classification (ASJC) codes

Nuclear and High Energy Physics

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10.1016/0550-3213(83)90053-6

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title = "On the renormalized coupling constant and the susceptibility in φ44 field theory and the Ising model in four dimensions",

abstract = "We discuss the euclidean φ44 field theory, and the critical behavior in ferromagnetic systems in four dimensions. It is rigorously shown that there are at most logarithmic corrections to the mean field law in the behavior of the magnetic susceptibility X = ΣS2(0, x). Furthermore, if any such corrections are present in a continuum limit which is used to construct a φ44 field theory, the limiting theory would be non-interacting. Our analysis extends to ferromagnetic systems of variables which belong to the Griffiths-Simon class.",

author = "Michael Aizenman and Ross Graham",

note = "Funding Information: i Sloan Foundation Research Fellow, supported by NSF grant PHY-8301493. Part of this work was done at the Princeton University, Physics Department, supported by NSF Grant PHY-8116101. 2 Current address: Defense Research Establishment Atlantic, P.O. Box 1012, Dartmouth, Nova Scotia B2Y 3Z7, Canada.",

year = "1983",

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doi = "10.1016/0550-3213(83)90053-6",

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T1 - On the renormalized coupling constant and the susceptibility in φ44 field theory and the Ising model in four dimensions

AU - Aizenman, Michael

AU - Graham, Ross

N1 - Funding Information: i Sloan Foundation Research Fellow, supported by NSF grant PHY-8301493. Part of this work was done at the Princeton University, Physics Department, supported by NSF Grant PHY-8116101. 2 Current address: Defense Research Establishment Atlantic, P.O. Box 1012, Dartmouth, Nova Scotia B2Y 3Z7, Canada.

PY - 1983/10/31

Y1 - 1983/10/31

N2 - We discuss the euclidean φ44 field theory, and the critical behavior in ferromagnetic systems in four dimensions. It is rigorously shown that there are at most logarithmic corrections to the mean field law in the behavior of the magnetic susceptibility X = ΣS2(0, x). Furthermore, if any such corrections are present in a continuum limit which is used to construct a φ44 field theory, the limiting theory would be non-interacting. Our analysis extends to ferromagnetic systems of variables which belong to the Griffiths-Simon class.

AB - We discuss the euclidean φ44 field theory, and the critical behavior in ferromagnetic systems in four dimensions. It is rigorously shown that there are at most logarithmic corrections to the mean field law in the behavior of the magnetic susceptibility X = ΣS2(0, x). Furthermore, if any such corrections are present in a continuum limit which is used to construct a φ44 field theory, the limiting theory would be non-interacting. Our analysis extends to ferromagnetic systems of variables which belong to the Griffiths-Simon class.

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